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fuzz_feedback.cpp
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fuzz_feedback.cpp
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/*
* ____ ____ _____
* | _ \| _ \| ___| _ ________
* | |_) | |_) | |_ | | | |_ /_ /
* | _ <| _ <| _|| |_| |/ / / /
* |_| \_\_| \_\_| \__,_/___/___|
*
* Copyright (C) National University of Singapore
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
/****************************************************************************/
/* TLSH */
/****************************************************************************/
/* ===========
* BSD License
* ===========
* Copyright (c) 2013, Trend Micro Incorporated
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. Neither the name of the copyright holder nor the names of its
* contributors may be used to endorse or promote products derived from this
* software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
* IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
* THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#define BUCKETS_128
#define TLSH_OPTION_CONSERVATIVE 2
#define TLSH_OPTION_KEEP_BUCKET 4
#define TLSH_OPTION_PRIVATE 8
#define TLSH_OPTION_THREADED 16
// Define TLSH_STRING_LEN_REQ, which is the string length of "T1" + the hex
// value of the Tlsh hash. BUCKETS_256 & CHECKSUM_3B are compiler switches
// defined in CMakeLists.txt
#if defined BUCKETS_256
#define TLSH_STRING_LEN_REQ 136
// changed the minimum data length to 256 for version 3.3
#define MIN_DATA_LENGTH 50
// added the -force option for version 3.5
// added the -conservatibe option for version 3.17
#define MIN_CONSERVATIVE_DATA_LENGTH 256
#endif
#if defined BUCKETS_128
#define TLSH_STRING_LEN_REQ 72
// changed the minimum data length to 256 for version 3.3
#define MIN_DATA_LENGTH 50
// added the -force option for version 3.5
// added the -conservatibe option for version 3.17
#define MIN_CONSERVATIVE_DATA_LENGTH 256
#endif
#if defined BUCKETS_48
// No 3 Byte checksum option for 48 Bucket min hash
#define TLSH_STRING_LEN 30
// changed the minimum data length to 256 for version 3.3
#define MIN_DATA_LENGTH 10
// added the -force option for version 3.5
#define MIN_CONSERVATIVE_DATA_LENGTH 10
#endif
#define TLSH_STRING_SIZE (TLSH_STRING_LEN_REQ + 1)
typedef struct TlshImpl TlshImpl;
typedef struct Tlsh TLSH;
static int tlsh_update(Tlsh* tlsh, const uint8_t *data, size_t len);
static int tlsh_final(Tlsh* tlsh, const uint8_t *data, size_t len);
#define SLIDING_WND_SIZE 5
#define BUCKETS 256
#define Q_BITS 2 // 2 bits; quartile value 0, 1, 2, 3
// BUCKETS_256 & CHECKSUM_3B are compiler switches defined in CMakeLists.txt
#if defined BUCKETS_256
#define EFF_BUCKETS 256
#define CODE_SIZE 64 // 256 * 2 bits = 64 bytes
#if defined CHECKSUM_3B
#define INTERNAL_TLSH_STRING_LEN 138
#define TLSH_CHECKSUM_LEN 3
// defined in tlsh.h #define TLSH_STRING_LEN 138 // 2 + 3 + 64 bytes = 138
// hexidecimal chars
#else
#define INTERNAL_TLSH_STRING_LEN 134
#define TLSH_CHECKSUM_LEN 1
// defined in tlsh.h #define TLSH_STRING_LEN 134 // 2 + 1 + 64 bytes = 134
// hexidecimal chars
#endif
#endif
#if defined BUCKETS_128
#define EFF_BUCKETS 128
#define CODE_SIZE 32 // 128 * 2 bits = 32 bytes
#if defined CHECKSUM_3B
#define INTERNAL_TLSH_STRING_LEN 74
#define TLSH_CHECKSUM_LEN 3
// defined in tlsh.h #define TLSH_STRING_LEN 74 // 2 + 3 + 32 bytes = 74
// hexidecimal chars
#else
#define INTERNAL_TLSH_STRING_LEN 70
#define TLSH_CHECKSUM_LEN 1
// defined in tlsh.h #define TLSH_STRING_LEN 70 // 2 + 1 + 32 bytes = 70
// hexidecimal chars
#endif
#endif
#if defined BUCKETS_48
#define INTERNAL_TLSH_STRING_LEN 33
#define EFF_BUCKETS 48
#define CODE_SIZE 12 // 48 * 2 bits = 12 bytes
#define TLSH_CHECKSUM_LEN 1
// defined in tlsh.h #define TLSH_STRING_LEN 30 // 2 + 1 + 12 bytes = 30
// hexidecimal chars
#endif
typedef struct {
unsigned char checksum[TLSH_CHECKSUM_LEN];
unsigned char lvalue;
union {
unsigned char qb;
struct {
unsigned char q1ratio : 4;
unsigned char q2ratio : 4;
} QR;
} Q;
unsigned char tmp_code[CODE_SIZE];
} LshBinStruct;
typedef struct TlshImpl {
unsigned int a_bucket[BUCKETS];
unsigned char slide_window[SLIDING_WND_SIZE];
unsigned int data_len;
LshBinStruct lsh_bin;
char *lsh_code;
bool lsh_code_valid;
} TlshImpl;
typedef struct Tlsh {
TlshImpl impl;
} Tlsh;
static int tlsh_impl_update(TlshImpl *impl, const unsigned char *data, unsigned int len, int tlsh_option);
static void tlsh_impl_final(TlshImpl *impl, int fc_cons_option);
static void tlsh_impl_reset(TlshImpl *impl);
static int tlsh_impl_is_valid(TlshImpl *impl);
static int tlsh_impl_compare(TlshImpl *impl, TlshImpl *other);
static int tlsh_impl_total_diff(TlshImpl *impl, TlshImpl *other, bool len_diff);
static int tlsh_impl_lvalue(TlshImpl *impl);
static int tlsh_impl_q1ratio(TlshImpl *impl);
static int tlsh_impl_q2ratio(TlshImpl *impl);
static int tlsh_impl_checksum(TlshImpl *impl, int k);
static int tlsh_impl_bucket_value(TlshImpl *impl, int bucket);
static int tlsh_impl_histogram_count(TlshImpl *impl, int bucket);
static int tlsh_impl_from_tlsh_str(TlshImpl *impl, const char *str);
static int tlsh_impl_hash(TlshImpl *impl, bool showvers, char *str, size_t size);
static unsigned char bit_pairs_diff_table[][256] = {
{0, 1, 2, 6, 1, 2, 3, 7, 2, 3, 4, 8, 6, 7, 8, 12, 1, 2, 3, 7, 2, 3, 4, 8,
3, 4, 5, 9, 7, 8, 9, 13, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14,
6, 7, 8, 12, 7, 8, 9, 13, 8, 9, 10, 14, 12, 13, 14, 18, 1, 2, 3, 7, 2, 3, 4, 8,
3, 4, 5, 9, 7, 8, 9, 13, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14,
3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11, 9, 10, 11, 15, 7, 8, 9, 13, 8, 9, 10, 14,
9, 10, 11, 15, 13, 14, 15, 19, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14,
3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11, 9, 10, 11, 15, 4, 5, 6, 10, 5, 6, 7, 11,
6, 7, 8, 12, 10, 11, 12, 16, 8, 9, 10, 14, 9, 10, 11, 15, 10, 11, 12, 16, 14, 15, 16, 20,
6, 7, 8, 12, 7, 8, 9, 13, 8, 9, 10, 14, 12, 13, 14, 18, 7, 8, 9, 13, 8, 9, 10, 14,
9, 10, 11, 15, 13, 14, 15, 19, 8, 9, 10, 14, 9, 10, 11, 15, 10, 11, 12, 16, 14, 15, 16, 20,
12, 13, 14, 18, 13, 14, 15, 19, 14, 15, 16, 20, 18, 19, 20, 24},
{1, 0, 1, 2, 2, 1, 2, 3, 3, 2, 3, 4, 7, 6, 7, 8, 2, 1, 2, 3, 3, 2, 3, 4,
4, 3, 4, 5, 8, 7, 8, 9, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10,
7, 6, 7, 8, 8, 7, 8, 9, 9, 8, 9, 10, 13, 12, 13, 14, 2, 1, 2, 3, 3, 2, 3, 4,
4, 3, 4, 5, 8, 7, 8, 9, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10,
4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 10, 9, 10, 11, 8, 7, 8, 9, 9, 8, 9, 10,
10, 9, 10, 11, 14, 13, 14, 15, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10,
4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 10, 9, 10, 11, 5, 4, 5, 6, 6, 5, 6, 7,
7, 6, 7, 8, 11, 10, 11, 12, 9, 8, 9, 10, 10, 9, 10, 11, 11, 10, 11, 12, 15, 14, 15, 16,
7, 6, 7, 8, 8, 7, 8, 9, 9, 8, 9, 10, 13, 12, 13, 14, 8, 7, 8, 9, 9, 8, 9, 10,
10, 9, 10, 11, 14, 13, 14, 15, 9, 8, 9, 10, 10, 9, 10, 11, 11, 10, 11, 12, 15, 14, 15, 16,
13, 12, 13, 14, 14, 13, 14, 15, 15, 14, 15, 16, 19, 18, 19, 20},
{2, 1, 0, 1, 3, 2, 1, 2, 4, 3, 2, 3, 8, 7, 6, 7, 3, 2, 1, 2, 4, 3, 2, 3,
5, 4, 3, 4, 9, 8, 7, 8, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9,
8, 7, 6, 7, 9, 8, 7, 8, 10, 9, 8, 9, 14, 13, 12, 13, 3, 2, 1, 2, 4, 3, 2, 3,
5, 4, 3, 4, 9, 8, 7, 8, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9,
5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 11, 10, 9, 10, 9, 8, 7, 8, 10, 9, 8, 9,
11, 10, 9, 10, 15, 14, 13, 14, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9,
5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 11, 10, 9, 10, 6, 5, 4, 5, 7, 6, 5, 6,
8, 7, 6, 7, 12, 11, 10, 11, 10, 9, 8, 9, 11, 10, 9, 10, 12, 11, 10, 11, 16, 15, 14, 15,
8, 7, 6, 7, 9, 8, 7, 8, 10, 9, 8, 9, 14, 13, 12, 13, 9, 8, 7, 8, 10, 9, 8, 9,
11, 10, 9, 10, 15, 14, 13, 14, 10, 9, 8, 9, 11, 10, 9, 10, 12, 11, 10, 11, 16, 15, 14, 15,
14, 13, 12, 13, 15, 14, 13, 14, 16, 15, 14, 15, 20, 19, 18, 19},
{6, 2, 1, 0, 7, 3, 2, 1, 8, 4, 3, 2, 12, 8, 7, 6, 7, 3, 2, 1, 8, 4, 3, 2,
9, 5, 4, 3, 13, 9, 8, 7, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8,
12, 8, 7, 6, 13, 9, 8, 7, 14, 10, 9, 8, 18, 14, 13, 12, 7, 3, 2, 1, 8, 4, 3, 2,
9, 5, 4, 3, 13, 9, 8, 7, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8,
9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5, 15, 11, 10, 9, 13, 9, 8, 7, 14, 10, 9, 8,
15, 11, 10, 9, 19, 15, 14, 13, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8,
9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5, 15, 11, 10, 9, 10, 6, 5, 4, 11, 7, 6, 5,
12, 8, 7, 6, 16, 12, 11, 10, 14, 10, 9, 8, 15, 11, 10, 9, 16, 12, 11, 10, 20, 16, 15, 14,
12, 8, 7, 6, 13, 9, 8, 7, 14, 10, 9, 8, 18, 14, 13, 12, 13, 9, 8, 7, 14, 10, 9, 8,
15, 11, 10, 9, 19, 15, 14, 13, 14, 10, 9, 8, 15, 11, 10, 9, 16, 12, 11, 10, 20, 16, 15, 14,
18, 14, 13, 12, 19, 15, 14, 13, 20, 16, 15, 14, 24, 20, 19, 18},
{1, 2, 3, 7, 0, 1, 2, 6, 1, 2, 3, 7, 2, 3, 4, 8, 2, 3, 4, 8, 1, 2, 3, 7,
2, 3, 4, 8, 3, 4, 5, 9, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10,
7, 8, 9, 13, 6, 7, 8, 12, 7, 8, 9, 13, 8, 9, 10, 14, 2, 3, 4, 8, 1, 2, 3, 7,
2, 3, 4, 8, 3, 4, 5, 9, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10,
4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11, 8, 9, 10, 14, 7, 8, 9, 13,
8, 9, 10, 14, 9, 10, 11, 15, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10,
4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11, 5, 6, 7, 11, 4, 5, 6, 10,
5, 6, 7, 11, 6, 7, 8, 12, 9, 10, 11, 15, 8, 9, 10, 14, 9, 10, 11, 15, 10, 11, 12, 16,
7, 8, 9, 13, 6, 7, 8, 12, 7, 8, 9, 13, 8, 9, 10, 14, 8, 9, 10, 14, 7, 8, 9, 13,
8, 9, 10, 14, 9, 10, 11, 15, 9, 10, 11, 15, 8, 9, 10, 14, 9, 10, 11, 15, 10, 11, 12, 16,
13, 14, 15, 19, 12, 13, 14, 18, 13, 14, 15, 19, 14, 15, 16, 20},
{2, 1, 2, 3, 1, 0, 1, 2, 2, 1, 2, 3, 3, 2, 3, 4, 3, 2, 3, 4, 2, 1, 2, 3,
3, 2, 3, 4, 4, 3, 4, 5, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6,
8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9, 9, 8, 9, 10, 3, 2, 3, 4, 2, 1, 2, 3,
3, 2, 3, 4, 4, 3, 4, 5, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6,
5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 9, 8, 9, 10, 8, 7, 8, 9,
9, 8, 9, 10, 10, 9, 10, 11, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6,
5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 6, 5, 6, 7, 5, 4, 5, 6,
6, 5, 6, 7, 7, 6, 7, 8, 10, 9, 10, 11, 9, 8, 9, 10, 10, 9, 10, 11, 11, 10, 11, 12,
8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9, 9, 8, 9, 10, 9, 8, 9, 10, 8, 7, 8, 9,
9, 8, 9, 10, 10, 9, 10, 11, 10, 9, 10, 11, 9, 8, 9, 10, 10, 9, 10, 11, 11, 10, 11, 12,
14, 13, 14, 15, 13, 12, 13, 14, 14, 13, 14, 15, 15, 14, 15, 16},
{3, 2, 1, 2, 2, 1, 0, 1, 3, 2, 1, 2, 4, 3, 2, 3, 4, 3, 2, 3, 3, 2, 1, 2,
4, 3, 2, 3, 5, 4, 3, 4, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5,
9, 8, 7, 8, 8, 7, 6, 7, 9, 8, 7, 8, 10, 9, 8, 9, 4, 3, 2, 3, 3, 2, 1, 2,
4, 3, 2, 3, 5, 4, 3, 4, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5,
6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 10, 9, 8, 9, 9, 8, 7, 8,
10, 9, 8, 9, 11, 10, 9, 10, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5,
6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 7, 6, 5, 6, 6, 5, 4, 5,
7, 6, 5, 6, 8, 7, 6, 7, 11, 10, 9, 10, 10, 9, 8, 9, 11, 10, 9, 10, 12, 11, 10, 11,
9, 8, 7, 8, 8, 7, 6, 7, 9, 8, 7, 8, 10, 9, 8, 9, 10, 9, 8, 9, 9, 8, 7, 8,
10, 9, 8, 9, 11, 10, 9, 10, 11, 10, 9, 10, 10, 9, 8, 9, 11, 10, 9, 10, 12, 11, 10, 11,
15, 14, 13, 14, 14, 13, 12, 13, 15, 14, 13, 14, 16, 15, 14, 15},
{7, 3, 2, 1, 6, 2, 1, 0, 7, 3, 2, 1, 8, 4, 3, 2, 8, 4, 3, 2, 7, 3, 2, 1,
8, 4, 3, 2, 9, 5, 4, 3, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4,
13, 9, 8, 7, 12, 8, 7, 6, 13, 9, 8, 7, 14, 10, 9, 8, 8, 4, 3, 2, 7, 3, 2, 1,
8, 4, 3, 2, 9, 5, 4, 3, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4,
10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5, 14, 10, 9, 8, 13, 9, 8, 7,
14, 10, 9, 8, 15, 11, 10, 9, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4,
10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5, 11, 7, 6, 5, 10, 6, 5, 4,
11, 7, 6, 5, 12, 8, 7, 6, 15, 11, 10, 9, 14, 10, 9, 8, 15, 11, 10, 9, 16, 12, 11, 10,
13, 9, 8, 7, 12, 8, 7, 6, 13, 9, 8, 7, 14, 10, 9, 8, 14, 10, 9, 8, 13, 9, 8, 7,
14, 10, 9, 8, 15, 11, 10, 9, 15, 11, 10, 9, 14, 10, 9, 8, 15, 11, 10, 9, 16, 12, 11, 10,
19, 15, 14, 13, 18, 14, 13, 12, 19, 15, 14, 13, 20, 16, 15, 14},
{2, 3, 4, 8, 1, 2, 3, 7, 0, 1, 2, 6, 1, 2, 3, 7, 3, 4, 5, 9, 2, 3, 4, 8,
1, 2, 3, 7, 2, 3, 4, 8, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9,
8, 9, 10, 14, 7, 8, 9, 13, 6, 7, 8, 12, 7, 8, 9, 13, 3, 4, 5, 9, 2, 3, 4, 8,
1, 2, 3, 7, 2, 3, 4, 8, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9,
5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10, 9, 10, 11, 15, 8, 9, 10, 14,
7, 8, 9, 13, 8, 9, 10, 14, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9,
5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10, 6, 7, 8, 12, 5, 6, 7, 11,
4, 5, 6, 10, 5, 6, 7, 11, 10, 11, 12, 16, 9, 10, 11, 15, 8, 9, 10, 14, 9, 10, 11, 15,
8, 9, 10, 14, 7, 8, 9, 13, 6, 7, 8, 12, 7, 8, 9, 13, 9, 10, 11, 15, 8, 9, 10, 14,
7, 8, 9, 13, 8, 9, 10, 14, 10, 11, 12, 16, 9, 10, 11, 15, 8, 9, 10, 14, 9, 10, 11, 15,
14, 15, 16, 20, 13, 14, 15, 19, 12, 13, 14, 18, 13, 14, 15, 19},
{3, 2, 3, 4, 2, 1, 2, 3, 1, 0, 1, 2, 2, 1, 2, 3, 4, 3, 4, 5, 3, 2, 3, 4,
2, 1, 2, 3, 3, 2, 3, 4, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5,
9, 8, 9, 10, 8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9, 4, 3, 4, 5, 3, 2, 3, 4,
2, 1, 2, 3, 3, 2, 3, 4, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5,
6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 10, 9, 10, 11, 9, 8, 9, 10,
8, 7, 8, 9, 9, 8, 9, 10, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5,
6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 7, 6, 7, 8, 6, 5, 6, 7,
5, 4, 5, 6, 6, 5, 6, 7, 11, 10, 11, 12, 10, 9, 10, 11, 9, 8, 9, 10, 10, 9, 10, 11,
9, 8, 9, 10, 8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9, 10, 9, 10, 11, 9, 8, 9, 10,
8, 7, 8, 9, 9, 8, 9, 10, 11, 10, 11, 12, 10, 9, 10, 11, 9, 8, 9, 10, 10, 9, 10, 11,
15, 14, 15, 16, 14, 13, 14, 15, 13, 12, 13, 14, 14, 13, 14, 15},
{4, 3, 2, 3, 3, 2, 1, 2, 2, 1, 0, 1, 3, 2, 1, 2, 5, 4, 3, 4, 4, 3, 2, 3,
3, 2, 1, 2, 4, 3, 2, 3, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4,
10, 9, 8, 9, 9, 8, 7, 8, 8, 7, 6, 7, 9, 8, 7, 8, 5, 4, 3, 4, 4, 3, 2, 3,
3, 2, 1, 2, 4, 3, 2, 3, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4,
7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 11, 10, 9, 10, 10, 9, 8, 9,
9, 8, 7, 8, 10, 9, 8, 9, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4,
7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 8, 7, 6, 7, 7, 6, 5, 6,
6, 5, 4, 5, 7, 6, 5, 6, 12, 11, 10, 11, 11, 10, 9, 10, 10, 9, 8, 9, 11, 10, 9, 10,
10, 9, 8, 9, 9, 8, 7, 8, 8, 7, 6, 7, 9, 8, 7, 8, 11, 10, 9, 10, 10, 9, 8, 9,
9, 8, 7, 8, 10, 9, 8, 9, 12, 11, 10, 11, 11, 10, 9, 10, 10, 9, 8, 9, 11, 10, 9, 10,
16, 15, 14, 15, 15, 14, 13, 14, 14, 13, 12, 13, 15, 14, 13, 14},
{8, 4, 3, 2, 7, 3, 2, 1, 6, 2, 1, 0, 7, 3, 2, 1, 9, 5, 4, 3, 8, 4, 3, 2,
7, 3, 2, 1, 8, 4, 3, 2, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3,
14, 10, 9, 8, 13, 9, 8, 7, 12, 8, 7, 6, 13, 9, 8, 7, 9, 5, 4, 3, 8, 4, 3, 2,
7, 3, 2, 1, 8, 4, 3, 2, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3,
11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4, 15, 11, 10, 9, 14, 10, 9, 8,
13, 9, 8, 7, 14, 10, 9, 8, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3,
11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4, 12, 8, 7, 6, 11, 7, 6, 5,
10, 6, 5, 4, 11, 7, 6, 5, 16, 12, 11, 10, 15, 11, 10, 9, 14, 10, 9, 8, 15, 11, 10, 9,
14, 10, 9, 8, 13, 9, 8, 7, 12, 8, 7, 6, 13, 9, 8, 7, 15, 11, 10, 9, 14, 10, 9, 8,
13, 9, 8, 7, 14, 10, 9, 8, 16, 12, 11, 10, 15, 11, 10, 9, 14, 10, 9, 8, 15, 11, 10, 9,
20, 16, 15, 14, 19, 15, 14, 13, 18, 14, 13, 12, 19, 15, 14, 13},
{6, 7, 8, 12, 2, 3, 4, 8, 1, 2, 3, 7, 0, 1, 2, 6, 7, 8, 9, 13, 3, 4, 5, 9,
2, 3, 4, 8, 1, 2, 3, 7, 8, 9, 10, 14, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8,
12, 13, 14, 18, 8, 9, 10, 14, 7, 8, 9, 13, 6, 7, 8, 12, 7, 8, 9, 13, 3, 4, 5, 9,
2, 3, 4, 8, 1, 2, 3, 7, 8, 9, 10, 14, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8,
9, 10, 11, 15, 5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9, 13, 14, 15, 19, 9, 10, 11, 15,
8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8,
9, 10, 11, 15, 5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9, 10, 11, 12, 16, 6, 7, 8, 12,
5, 6, 7, 11, 4, 5, 6, 10, 14, 15, 16, 20, 10, 11, 12, 16, 9, 10, 11, 15, 8, 9, 10, 14,
12, 13, 14, 18, 8, 9, 10, 14, 7, 8, 9, 13, 6, 7, 8, 12, 13, 14, 15, 19, 9, 10, 11, 15,
8, 9, 10, 14, 7, 8, 9, 13, 14, 15, 16, 20, 10, 11, 12, 16, 9, 10, 11, 15, 8, 9, 10, 14,
18, 19, 20, 24, 14, 15, 16, 20, 13, 14, 15, 19, 12, 13, 14, 18},
{7, 6, 7, 8, 3, 2, 3, 4, 2, 1, 2, 3, 1, 0, 1, 2, 8, 7, 8, 9, 4, 3, 4, 5,
3, 2, 3, 4, 2, 1, 2, 3, 9, 8, 9, 10, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4,
13, 12, 13, 14, 9, 8, 9, 10, 8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9, 4, 3, 4, 5,
3, 2, 3, 4, 2, 1, 2, 3, 9, 8, 9, 10, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4,
10, 9, 10, 11, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 14, 13, 14, 15, 10, 9, 10, 11,
9, 8, 9, 10, 8, 7, 8, 9, 9, 8, 9, 10, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4,
10, 9, 10, 11, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 11, 10, 11, 12, 7, 6, 7, 8,
6, 5, 6, 7, 5, 4, 5, 6, 15, 14, 15, 16, 11, 10, 11, 12, 10, 9, 10, 11, 9, 8, 9, 10,
13, 12, 13, 14, 9, 8, 9, 10, 8, 7, 8, 9, 7, 6, 7, 8, 14, 13, 14, 15, 10, 9, 10, 11,
9, 8, 9, 10, 8, 7, 8, 9, 15, 14, 15, 16, 11, 10, 11, 12, 10, 9, 10, 11, 9, 8, 9, 10,
19, 18, 19, 20, 15, 14, 15, 16, 14, 13, 14, 15, 13, 12, 13, 14},
{8, 7, 6, 7, 4, 3, 2, 3, 3, 2, 1, 2, 2, 1, 0, 1, 9, 8, 7, 8, 5, 4, 3, 4,
4, 3, 2, 3, 3, 2, 1, 2, 10, 9, 8, 9, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3,
14, 13, 12, 13, 10, 9, 8, 9, 9, 8, 7, 8, 8, 7, 6, 7, 9, 8, 7, 8, 5, 4, 3, 4,
4, 3, 2, 3, 3, 2, 1, 2, 10, 9, 8, 9, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3,
11, 10, 9, 10, 7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4, 15, 14, 13, 14, 11, 10, 9, 10,
10, 9, 8, 9, 9, 8, 7, 8, 10, 9, 8, 9, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3,
11, 10, 9, 10, 7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4, 12, 11, 10, 11, 8, 7, 6, 7,
7, 6, 5, 6, 6, 5, 4, 5, 16, 15, 14, 15, 12, 11, 10, 11, 11, 10, 9, 10, 10, 9, 8, 9,
14, 13, 12, 13, 10, 9, 8, 9, 9, 8, 7, 8, 8, 7, 6, 7, 15, 14, 13, 14, 11, 10, 9, 10,
10, 9, 8, 9, 9, 8, 7, 8, 16, 15, 14, 15, 12, 11, 10, 11, 11, 10, 9, 10, 10, 9, 8, 9,
20, 19, 18, 19, 16, 15, 14, 15, 15, 14, 13, 14, 14, 13, 12, 13},
{12, 8, 7, 6, 8, 4, 3, 2, 7, 3, 2, 1, 6, 2, 1, 0, 13, 9, 8, 7, 9, 5, 4, 3,
8, 4, 3, 2, 7, 3, 2, 1, 14, 10, 9, 8, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2,
18, 14, 13, 12, 14, 10, 9, 8, 13, 9, 8, 7, 12, 8, 7, 6, 13, 9, 8, 7, 9, 5, 4, 3,
8, 4, 3, 2, 7, 3, 2, 1, 14, 10, 9, 8, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2,
15, 11, 10, 9, 11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3, 19, 15, 14, 13, 15, 11, 10, 9,
14, 10, 9, 8, 13, 9, 8, 7, 14, 10, 9, 8, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2,
15, 11, 10, 9, 11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3, 16, 12, 11, 10, 12, 8, 7, 6,
11, 7, 6, 5, 10, 6, 5, 4, 20, 16, 15, 14, 16, 12, 11, 10, 15, 11, 10, 9, 14, 10, 9, 8,
18, 14, 13, 12, 14, 10, 9, 8, 13, 9, 8, 7, 12, 8, 7, 6, 19, 15, 14, 13, 15, 11, 10, 9,
14, 10, 9, 8, 13, 9, 8, 7, 20, 16, 15, 14, 16, 12, 11, 10, 15, 11, 10, 9, 14, 10, 9, 8,
24, 20, 19, 18, 20, 16, 15, 14, 19, 15, 14, 13, 18, 14, 13, 12},
{1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 7, 8, 9, 13, 0, 1, 2, 6, 1, 2, 3, 7,
2, 3, 4, 8, 6, 7, 8, 12, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 7, 8, 9, 13,
2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14, 2, 3, 4, 8, 3, 4, 5, 9,
4, 5, 6, 10, 8, 9, 10, 14, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 7, 8, 9, 13,
2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14, 3, 4, 5, 9, 4, 5, 6, 10,
5, 6, 7, 11, 9, 10, 11, 15, 3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11, 9, 10, 11, 15,
2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14, 3, 4, 5, 9, 4, 5, 6, 10,
5, 6, 7, 11, 9, 10, 11, 15, 4, 5, 6, 10, 5, 6, 7, 11, 6, 7, 8, 12, 10, 11, 12, 16,
7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15, 13, 14, 15, 19, 6, 7, 8, 12, 7, 8, 9, 13,
8, 9, 10, 14, 12, 13, 14, 18, 7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15, 13, 14, 15, 19,
8, 9, 10, 14, 9, 10, 11, 15, 10, 11, 12, 16, 14, 15, 16, 20},
{2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 8, 7, 8, 9, 1, 0, 1, 2, 2, 1, 2, 3,
3, 2, 3, 4, 7, 6, 7, 8, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 8, 7, 8, 9,
3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10, 3, 2, 3, 4, 4, 3, 4, 5,
5, 4, 5, 6, 9, 8, 9, 10, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 8, 7, 8, 9,
3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10, 4, 3, 4, 5, 5, 4, 5, 6,
6, 5, 6, 7, 10, 9, 10, 11, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 10, 9, 10, 11,
3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10, 4, 3, 4, 5, 5, 4, 5, 6,
6, 5, 6, 7, 10, 9, 10, 11, 5, 4, 5, 6, 6, 5, 6, 7, 7, 6, 7, 8, 11, 10, 11, 12,
8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11, 14, 13, 14, 15, 7, 6, 7, 8, 8, 7, 8, 9,
9, 8, 9, 10, 13, 12, 13, 14, 8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11, 14, 13, 14, 15,
9, 8, 9, 10, 10, 9, 10, 11, 11, 10, 11, 12, 15, 14, 15, 16},
{3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 9, 8, 7, 8, 2, 1, 0, 1, 3, 2, 1, 2,
4, 3, 2, 3, 8, 7, 6, 7, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 9, 8, 7, 8,
4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9, 4, 3, 2, 3, 5, 4, 3, 4,
6, 5, 4, 5, 10, 9, 8, 9, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 9, 8, 7, 8,
4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9, 5, 4, 3, 4, 6, 5, 4, 5,
7, 6, 5, 6, 11, 10, 9, 10, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 11, 10, 9, 10,
4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9, 5, 4, 3, 4, 6, 5, 4, 5,
7, 6, 5, 6, 11, 10, 9, 10, 6, 5, 4, 5, 7, 6, 5, 6, 8, 7, 6, 7, 12, 11, 10, 11,
9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10, 15, 14, 13, 14, 8, 7, 6, 7, 9, 8, 7, 8,
10, 9, 8, 9, 14, 13, 12, 13, 9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10, 15, 14, 13, 14,
10, 9, 8, 9, 11, 10, 9, 10, 12, 11, 10, 11, 16, 15, 14, 15},
{7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 13, 9, 8, 7, 6, 2, 1, 0, 7, 3, 2, 1,
8, 4, 3, 2, 12, 8, 7, 6, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 13, 9, 8, 7,
8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8, 8, 4, 3, 2, 9, 5, 4, 3,
10, 6, 5, 4, 14, 10, 9, 8, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 13, 9, 8, 7,
8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8, 9, 5, 4, 3, 10, 6, 5, 4,
11, 7, 6, 5, 15, 11, 10, 9, 9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5, 15, 11, 10, 9,
8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8, 9, 5, 4, 3, 10, 6, 5, 4,
11, 7, 6, 5, 15, 11, 10, 9, 10, 6, 5, 4, 11, 7, 6, 5, 12, 8, 7, 6, 16, 12, 11, 10,
13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9, 19, 15, 14, 13, 12, 8, 7, 6, 13, 9, 8, 7,
14, 10, 9, 8, 18, 14, 13, 12, 13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9, 19, 15, 14, 13,
14, 10, 9, 8, 15, 11, 10, 9, 16, 12, 11, 10, 20, 16, 15, 14},
{2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 1, 2, 3, 7, 0, 1, 2, 6,
1, 2, 3, 7, 2, 3, 4, 8, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9,
3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8,
3, 4, 5, 9, 4, 5, 6, 10, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9,
3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 4, 5, 6, 10, 3, 4, 5, 9,
4, 5, 6, 10, 5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11,
3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 4, 5, 6, 10, 3, 4, 5, 9,
4, 5, 6, 10, 5, 6, 7, 11, 5, 6, 7, 11, 4, 5, 6, 10, 5, 6, 7, 11, 6, 7, 8, 12,
8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15, 7, 8, 9, 13, 6, 7, 8, 12,
7, 8, 9, 13, 8, 9, 10, 14, 8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15,
9, 10, 11, 15, 8, 9, 10, 14, 9, 10, 11, 15, 10, 11, 12, 16},
{3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 2, 1, 2, 3, 1, 0, 1, 2,
2, 1, 2, 3, 3, 2, 3, 4, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5,
4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4,
4, 3, 4, 5, 5, 4, 5, 6, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5,
4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 5, 4, 5, 6, 4, 3, 4, 5,
5, 4, 5, 6, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7,
4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 5, 4, 5, 6, 4, 3, 4, 5,
5, 4, 5, 6, 6, 5, 6, 7, 6, 5, 6, 7, 5, 4, 5, 6, 6, 5, 6, 7, 7, 6, 7, 8,
9, 8, 9, 10, 8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11, 8, 7, 8, 9, 7, 6, 7, 8,
8, 7, 8, 9, 9, 8, 9, 10, 9, 8, 9, 10, 8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11,
10, 9, 10, 11, 9, 8, 9, 10, 10, 9, 10, 11, 11, 10, 11, 12},
{4, 3, 2, 3, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 3, 2, 1, 2, 2, 1, 0, 1,
3, 2, 1, 2, 4, 3, 2, 3, 4, 3, 2, 3, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4,
5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3,
5, 4, 3, 4, 6, 5, 4, 5, 4, 3, 2, 3, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4,
5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 6, 5, 4, 5, 5, 4, 3, 4,
6, 5, 4, 5, 7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6,
5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 6, 5, 4, 5, 5, 4, 3, 4,
6, 5, 4, 5, 7, 6, 5, 6, 7, 6, 5, 6, 6, 5, 4, 5, 7, 6, 5, 6, 8, 7, 6, 7,
10, 9, 8, 9, 9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10, 9, 8, 7, 8, 8, 7, 6, 7,
9, 8, 7, 8, 10, 9, 8, 9, 10, 9, 8, 9, 9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10,
11, 10, 9, 10, 10, 9, 8, 9, 11, 10, 9, 10, 12, 11, 10, 11},
{8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 7, 3, 2, 1, 6, 2, 1, 0,
7, 3, 2, 1, 8, 4, 3, 2, 8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3,
9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2,
9, 5, 4, 3, 10, 6, 5, 4, 8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3,
9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 10, 6, 5, 4, 9, 5, 4, 3,
10, 6, 5, 4, 11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5,
9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 10, 6, 5, 4, 9, 5, 4, 3,
10, 6, 5, 4, 11, 7, 6, 5, 11, 7, 6, 5, 10, 6, 5, 4, 11, 7, 6, 5, 12, 8, 7, 6,
14, 10, 9, 8, 13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9, 13, 9, 8, 7, 12, 8, 7, 6,
13, 9, 8, 7, 14, 10, 9, 8, 14, 10, 9, 8, 13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9,
15, 11, 10, 9, 14, 10, 9, 8, 15, 11, 10, 9, 16, 12, 11, 10},
{3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 2, 3, 4, 8, 1, 2, 3, 7,
0, 1, 2, 6, 1, 2, 3, 7, 3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8,
4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 3, 4, 5, 9,
2, 3, 4, 8, 3, 4, 5, 9, 3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8,
4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 5, 6, 7, 11, 4, 5, 6, 10,
3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10,
4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 5, 6, 7, 11, 4, 5, 6, 10,
3, 4, 5, 9, 4, 5, 6, 10, 6, 7, 8, 12, 5, 6, 7, 11, 4, 5, 6, 10, 5, 6, 7, 11,
9, 10, 11, 15, 8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14, 8, 9, 10, 14, 7, 8, 9, 13,
6, 7, 8, 12, 7, 8, 9, 13, 9, 10, 11, 15, 8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14,
10, 11, 12, 16, 9, 10, 11, 15, 8, 9, 10, 14, 9, 10, 11, 15},
{4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 3, 2, 3, 4, 2, 1, 2, 3, 1, 0,
1, 2, 2, 1, 2, 3, 4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 5, 4, 5, 6,
4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3,
4, 5, 4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 5, 4, 5, 6, 4, 3, 4, 5,
3, 2, 3, 4, 4, 3, 4, 5, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5,
6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4,
4, 3, 4, 5, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 7, 6, 7, 8, 6, 5,
6, 7, 5, 4, 5, 6, 6, 5, 6, 7, 10, 9, 10, 11, 9, 8, 9, 10, 8, 7, 8, 9, 9, 8, 9, 10,
9, 8, 9, 10, 8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9, 10, 9, 10, 11, 9, 8, 9, 10, 8, 7,
8, 9, 9, 8, 9, 10, 11, 10, 11, 12, 10, 9, 10, 11, 9, 8, 9, 10, 10, 9, 10, 11},
{5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2, 4, 3, 2, 3, 4, 3, 2, 3, 3, 2, 1, 2, 2, 1,
0, 1, 3, 2, 1, 2, 5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2, 4, 3, 2, 3, 6, 5, 4, 5,
5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4,
3, 4, 5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2, 4, 3, 2, 3, 6, 5, 4, 5, 5, 4, 3, 4,
4, 3, 2, 3, 5, 4, 3, 4, 7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6,
5, 6, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3,
5, 4, 3, 4, 7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 8, 7, 6, 7, 7, 6,
5, 6, 6, 5, 4, 5, 7, 6, 5, 6, 11, 10, 9, 10, 10, 9, 8, 9, 9, 8, 7, 8, 10, 9, 8, 9,
10, 9, 8, 9, 9, 8, 7, 8, 8, 7, 6, 7, 9, 8, 7, 8, 11, 10, 9, 10, 10, 9, 8, 9, 9, 8,
7, 8, 10, 9, 8, 9, 12, 11, 10, 11, 11, 10, 9, 10, 10, 9, 8, 9, 11, 10, 9, 10},
{9, 5, 4, 3, 8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2, 8, 4, 3, 2, 7, 3, 2, 1,
6, 2, 1, 0, 7, 3, 2, 1, 9, 5, 4, 3, 8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2,
10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 9, 5, 4, 3,
8, 4, 3, 2, 9, 5, 4, 3, 9, 5, 4, 3, 8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2,
10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 11, 7, 6, 5, 10, 6, 5, 4,
9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4,
10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 11, 7, 6, 5, 10, 6, 5, 4,
9, 5, 4, 3, 10, 6, 5, 4, 12, 8, 7, 6, 11, 7, 6, 5, 10, 6, 5, 4, 11, 7, 6, 5,
15, 11, 10, 9, 14, 10, 9, 8, 13, 9, 8, 7, 14, 10, 9, 8, 14, 10, 9, 8, 13, 9, 8, 7,
12, 8, 7, 6, 13, 9, 8, 7, 15, 11, 10, 9, 14, 10, 9, 8, 13, 9, 8, 7, 14, 10, 9, 8,
16, 12, 11, 10, 15, 11, 10, 9, 14, 10, 9, 8, 15, 11, 10, 9},
{7, 8, 9, 13, 3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7, 6, 7, 8, 12, 2, 3, 4, 8,
1, 2, 3, 7, 0, 1, 2, 6, 7, 8, 9, 13, 3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7,
8, 9, 10, 14, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 8, 9, 10, 14, 4, 5, 6, 10,
3, 4, 5, 9, 2, 3, 4, 8, 7, 8, 9, 13, 3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7,
8, 9, 10, 14, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 9, 10, 11, 15, 5, 6, 7, 11,
4, 5, 6, 10, 3, 4, 5, 9, 9, 10, 11, 15, 5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9,
8, 9, 10, 14, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 9, 10, 11, 15, 5, 6, 7, 11,
4, 5, 6, 10, 3, 4, 5, 9, 10, 11, 12, 16, 6, 7, 8, 12, 5, 6, 7, 11, 4, 5, 6, 10,
13, 14, 15, 19, 9, 10, 11, 15, 8, 9, 10, 14, 7, 8, 9, 13, 12, 13, 14, 18, 8, 9, 10, 14,
7, 8, 9, 13, 6, 7, 8, 12, 13, 14, 15, 19, 9, 10, 11, 15, 8, 9, 10, 14, 7, 8, 9, 13,
14, 15, 16, 20, 10, 11, 12, 16, 9, 10, 11, 15, 8, 9, 10, 14},
{8, 7, 8, 9, 4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 7, 6, 7, 8, 3, 2, 3, 4,
2, 1, 2, 3, 1, 0, 1, 2, 8, 7, 8, 9, 4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3,
9, 8, 9, 10, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 9, 8, 9, 10, 5, 4, 5, 6,
4, 3, 4, 5, 3, 2, 3, 4, 8, 7, 8, 9, 4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3,
9, 8, 9, 10, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 10, 9, 10, 11, 6, 5, 6, 7,
5, 4, 5, 6, 4, 3, 4, 5, 10, 9, 10, 11, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5,
9, 8, 9, 10, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 10, 9, 10, 11, 6, 5, 6, 7,
5, 4, 5, 6, 4, 3, 4, 5, 11, 10, 11, 12, 7, 6, 7, 8, 6, 5, 6, 7, 5, 4, 5, 6,
14, 13, 14, 15, 10, 9, 10, 11, 9, 8, 9, 10, 8, 7, 8, 9, 13, 12, 13, 14, 9, 8, 9, 10,
8, 7, 8, 9, 7, 6, 7, 8, 14, 13, 14, 15, 10, 9, 10, 11, 9, 8, 9, 10, 8, 7, 8, 9,
15, 14, 15, 16, 11, 10, 11, 12, 10, 9, 10, 11, 9, 8, 9, 10},
{9, 8, 7, 8, 5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2, 8, 7, 6, 7, 4, 3, 2, 3,
3, 2, 1, 2, 2, 1, 0, 1, 9, 8, 7, 8, 5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2,
10, 9, 8, 9, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 10, 9, 8, 9, 6, 5, 4, 5,
5, 4, 3, 4, 4, 3, 2, 3, 9, 8, 7, 8, 5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2,
10, 9, 8, 9, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 11, 10, 9, 10, 7, 6, 5, 6,
6, 5, 4, 5, 5, 4, 3, 4, 11, 10, 9, 10, 7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4,
10, 9, 8, 9, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 11, 10, 9, 10, 7, 6, 5, 6,
6, 5, 4, 5, 5, 4, 3, 4, 12, 11, 10, 11, 8, 7, 6, 7, 7, 6, 5, 6, 6, 5, 4, 5,
15, 14, 13, 14, 11, 10, 9, 10, 10, 9, 8, 9, 9, 8, 7, 8, 14, 13, 12, 13, 10, 9, 8, 9,
9, 8, 7, 8, 8, 7, 6, 7, 15, 14, 13, 14, 11, 10, 9, 10, 10, 9, 8, 9, 9, 8, 7, 8,
16, 15, 14, 15, 12, 11, 10, 11, 11, 10, 9, 10, 10, 9, 8, 9},
{13, 9, 8, 7, 9, 5, 4, 3, 8, 4, 3, 2, 7, 3, 2, 1, 12, 8, 7, 6, 8, 4, 3, 2,
7, 3, 2, 1, 6, 2, 1, 0, 13, 9, 8, 7, 9, 5, 4, 3, 8, 4, 3, 2, 7, 3, 2, 1,
14, 10, 9, 8, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 14, 10, 9, 8, 10, 6, 5, 4,
9, 5, 4, 3, 8, 4, 3, 2, 13, 9, 8, 7, 9, 5, 4, 3, 8, 4, 3, 2, 7, 3, 2, 1,
14, 10, 9, 8, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 15, 11, 10, 9, 11, 7, 6, 5,
10, 6, 5, 4, 9, 5, 4, 3, 15, 11, 10, 9, 11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3,
14, 10, 9, 8, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 15, 11, 10, 9, 11, 7, 6, 5,
10, 6, 5, 4, 9, 5, 4, 3, 16, 12, 11, 10, 12, 8, 7, 6, 11, 7, 6, 5, 10, 6, 5, 4,
19, 15, 14, 13, 15, 11, 10, 9, 14, 10, 9, 8, 13, 9, 8, 7, 18, 14, 13, 12, 14, 10, 9, 8,
13, 9, 8, 7, 12, 8, 7, 6, 19, 15, 14, 13, 15, 11, 10, 9, 14, 10, 9, 8, 13, 9, 8, 7,
20, 16, 15, 14, 16, 12, 11, 10, 15, 11, 10, 9, 14, 10, 9, 8},
{2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14, 1, 2, 3, 7, 2, 3, 4, 8,
3, 4, 5, 9, 7, 8, 9, 13, 0, 1, 2, 6, 1, 2, 3, 7, 2, 3, 4, 8, 6, 7, 8, 12,
1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 7, 8, 9, 13, 3, 4, 5, 9, 4, 5, 6, 10,
5, 6, 7, 11, 9, 10, 11, 15, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14,
1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 7, 8, 9, 13, 2, 3, 4, 8, 3, 4, 5, 9,
4, 5, 6, 10, 8, 9, 10, 14, 4, 5, 6, 10, 5, 6, 7, 11, 6, 7, 8, 12, 10, 11, 12, 16,
3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11, 9, 10, 11, 15, 2, 3, 4, 8, 3, 4, 5, 9,
4, 5, 6, 10, 8, 9, 10, 14, 3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11, 9, 10, 11, 15,
8, 9, 10, 14, 9, 10, 11, 15, 10, 11, 12, 16, 14, 15, 16, 20, 7, 8, 9, 13, 8, 9, 10, 14,
9, 10, 11, 15, 13, 14, 15, 19, 6, 7, 8, 12, 7, 8, 9, 13, 8, 9, 10, 14, 12, 13, 14, 18,
7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15, 13, 14, 15, 19},
{3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10, 2, 1, 2, 3, 3, 2, 3, 4,
4, 3, 4, 5, 8, 7, 8, 9, 1, 0, 1, 2, 2, 1, 2, 3, 3, 2, 3, 4, 7, 6, 7, 8,
2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 8, 7, 8, 9, 4, 3, 4, 5, 5, 4, 5, 6,
6, 5, 6, 7, 10, 9, 10, 11, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10,
2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 8, 7, 8, 9, 3, 2, 3, 4, 4, 3, 4, 5,
5, 4, 5, 6, 9, 8, 9, 10, 5, 4, 5, 6, 6, 5, 6, 7, 7, 6, 7, 8, 11, 10, 11, 12,
4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 10, 9, 10, 11, 3, 2, 3, 4, 4, 3, 4, 5,
5, 4, 5, 6, 9, 8, 9, 10, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 10, 9, 10, 11,
9, 8, 9, 10, 10, 9, 10, 11, 11, 10, 11, 12, 15, 14, 15, 16, 8, 7, 8, 9, 9, 8, 9, 10,
10, 9, 10, 11, 14, 13, 14, 15, 7, 6, 7, 8, 8, 7, 8, 9, 9, 8, 9, 10, 13, 12, 13, 14,
8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11, 14, 13, 14, 15},
{4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9, 3, 2, 1, 2, 4, 3, 2, 3,
5, 4, 3, 4, 9, 8, 7, 8, 2, 1, 0, 1, 3, 2, 1, 2, 4, 3, 2, 3, 8, 7, 6, 7,
3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 9, 8, 7, 8, 5, 4, 3, 4, 6, 5, 4, 5,
7, 6, 5, 6, 11, 10, 9, 10, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9,
3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 9, 8, 7, 8, 4, 3, 2, 3, 5, 4, 3, 4,
6, 5, 4, 5, 10, 9, 8, 9, 6, 5, 4, 5, 7, 6, 5, 6, 8, 7, 6, 7, 12, 11, 10, 11,
5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 11, 10, 9, 10, 4, 3, 2, 3, 5, 4, 3, 4,
6, 5, 4, 5, 10, 9, 8, 9, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 11, 10, 9, 10,
10, 9, 8, 9, 11, 10, 9, 10, 12, 11, 10, 11, 16, 15, 14, 15, 9, 8, 7, 8, 10, 9, 8, 9,
11, 10, 9, 10, 15, 14, 13, 14, 8, 7, 6, 7, 9, 8, 7, 8, 10, 9, 8, 9, 14, 13, 12, 13,
9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10, 15, 14, 13, 14},
{8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8, 7, 3, 2, 1, 8, 4, 3, 2,
9, 5, 4, 3, 13, 9, 8, 7, 6, 2, 1, 0, 7, 3, 2, 1, 8, 4, 3, 2, 12, 8, 7, 6,
7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 13, 9, 8, 7, 9, 5, 4, 3, 10, 6, 5, 4,
11, 7, 6, 5, 15, 11, 10, 9, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8,
7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 13, 9, 8, 7, 8, 4, 3, 2, 9, 5, 4, 3,
10, 6, 5, 4, 14, 10, 9, 8, 10, 6, 5, 4, 11, 7, 6, 5, 12, 8, 7, 6, 16, 12, 11, 10,
9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5, 15, 11, 10, 9, 8, 4, 3, 2, 9, 5, 4, 3,
10, 6, 5, 4, 14, 10, 9, 8, 9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5, 15, 11, 10, 9,
14, 10, 9, 8, 15, 11, 10, 9, 16, 12, 11, 10, 20, 16, 15, 14, 13, 9, 8, 7, 14, 10, 9, 8,
15, 11, 10, 9, 19, 15, 14, 13, 12, 8, 7, 6, 13, 9, 8, 7, 14, 10, 9, 8, 18, 14, 13, 12,
13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9, 19, 15, 14, 13},
{3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 2, 3, 4, 8, 1, 2, 3, 7,
2, 3, 4, 8, 3, 4, 5, 9, 1, 2, 3, 7, 0, 1, 2, 6, 1, 2, 3, 7, 2, 3, 4, 8,
2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 3, 4, 5, 9,
4, 5, 6, 10, 5, 6, 7, 11, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10,
2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 3, 4, 5, 9, 2, 3, 4, 8,
3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11, 4, 5, 6, 10, 5, 6, 7, 11, 6, 7, 8, 12,
4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11, 3, 4, 5, 9, 2, 3, 4, 8,
3, 4, 5, 9, 4, 5, 6, 10, 4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11,
9, 10, 11, 15, 8, 9, 10, 14, 9, 10, 11, 15, 10, 11, 12, 16, 8, 9, 10, 14, 7, 8, 9, 13,
8, 9, 10, 14, 9, 10, 11, 15, 7, 8, 9, 13, 6, 7, 8, 12, 7, 8, 9, 13, 8, 9, 10, 14,
8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15},
{4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2,
3, 4, 4, 3, 4, 5, 2, 1, 2, 3, 1, 0, 1, 2, 2, 1, 2, 3, 3, 2, 3, 4, 3, 2, 3, 4,
2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5,
6, 7, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 3, 2, 3, 4, 2, 1, 2, 3,
3, 2, 3, 4, 4, 3, 4, 5, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5,
6, 7, 5, 4, 5, 6, 6, 5, 6, 7, 7, 6, 7, 8, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6,
6, 5, 6, 7, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 5, 4, 5, 6, 4, 3,
4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 10, 9, 10, 11, 9, 8, 9, 10, 10, 9, 10, 11, 11, 10, 11, 12,
9, 8, 9, 10, 8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11, 8, 7, 8, 9, 7, 6, 7, 8, 8, 7,
8, 9, 9, 8, 9, 10, 9, 8, 9, 10, 8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11},
{5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 4, 3, 2, 3, 3, 2, 1, 2, 4, 3,
2, 3, 5, 4, 3, 4, 3, 2, 1, 2, 2, 1, 0, 1, 3, 2, 1, 2, 4, 3, 2, 3, 4, 3, 2, 3,
3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6,
5, 6, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 4, 3, 2, 3, 3, 2, 1, 2,
4, 3, 2, 3, 5, 4, 3, 4, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6,
5, 6, 6, 5, 4, 5, 7, 6, 5, 6, 8, 7, 6, 7, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5,
7, 6, 5, 6, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 6, 5, 4, 5, 5, 4,
3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 11, 10, 9, 10, 10, 9, 8, 9, 11, 10, 9, 10, 12, 11, 10, 11,
10, 9, 8, 9, 9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10, 9, 8, 7, 8, 8, 7, 6, 7, 9, 8,
7, 8, 10, 9, 8, 9, 10, 9, 8, 9, 9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10},
{9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 8, 4, 3, 2, 7, 3, 2, 1,
8, 4, 3, 2, 9, 5, 4, 3, 7, 3, 2, 1, 6, 2, 1, 0, 7, 3, 2, 1, 8, 4, 3, 2,
8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 9, 5, 4, 3,
10, 6, 5, 4, 11, 7, 6, 5, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4,
8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 9, 5, 4, 3, 8, 4, 3, 2,
9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5, 10, 6, 5, 4, 11, 7, 6, 5, 12, 8, 7, 6,
10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5, 9, 5, 4, 3, 8, 4, 3, 2,
9, 5, 4, 3, 10, 6, 5, 4, 10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5,
15, 11, 10, 9, 14, 10, 9, 8, 15, 11, 10, 9, 16, 12, 11, 10, 14, 10, 9, 8, 13, 9, 8, 7,
14, 10, 9, 8, 15, 11, 10, 9, 13, 9, 8, 7, 12, 8, 7, 6, 13, 9, 8, 7, 14, 10, 9, 8,
14, 10, 9, 8, 13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9},
{4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 3, 4, 5, 9, 2, 3, 4, 8,
1, 2, 3, 7, 2, 3, 4, 8, 2, 3, 4, 8, 1, 2, 3, 7, 0, 1, 2, 6, 1, 2, 3, 7,
3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 5, 6, 7, 11, 4, 5, 6, 10,
3, 4, 5, 9, 4, 5, 6, 10, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9,
3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 4, 5, 6, 10, 3, 4, 5, 9,
2, 3, 4, 8, 3, 4, 5, 9, 6, 7, 8, 12, 5, 6, 7, 11, 4, 5, 6, 10, 5, 6, 7, 11,
5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10, 4, 5, 6, 10, 3, 4, 5, 9,
2, 3, 4, 8, 3, 4, 5, 9, 5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10,
10, 11, 12, 16, 9, 10, 11, 15, 8, 9, 10, 14, 9, 10, 11, 15, 9, 10, 11, 15, 8, 9, 10, 14,
7, 8, 9, 13, 8, 9, 10, 14, 8, 9, 10, 14, 7, 8, 9, 13, 6, 7, 8, 12, 7, 8, 9, 13,
9, 10, 11, 15, 8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14},
{5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 4, 3, 4, 5, 3, 2, 3, 4,
2, 1, 2, 3, 3, 2, 3, 4, 3, 2, 3, 4, 2, 1, 2, 3, 1, 0, 1, 2, 2, 1, 2, 3,
4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 6, 5, 6, 7, 5, 4, 5, 6,
4, 3, 4, 5, 5, 4, 5, 6, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5,
4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 5, 4, 5, 6, 4, 3, 4, 5,
3, 2, 3, 4, 4, 3, 4, 5, 7, 6, 7, 8, 6, 5, 6, 7, 5, 4, 5, 6, 6, 5, 6, 7,
6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 5, 4, 5, 6, 4, 3, 4, 5,
3, 2, 3, 4, 4, 3, 4, 5, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6,
11, 10, 11, 12, 10, 9, 10, 11, 9, 8, 9, 10, 10, 9, 10, 11, 10, 9, 10, 11, 9, 8, 9, 10,
8, 7, 8, 9, 9, 8, 9, 10, 9, 8, 9, 10, 8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9,
10, 9, 10, 11, 9, 8, 9, 10, 8, 7, 8, 9, 9, 8, 9, 10},
{6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 5, 4, 3, 4, 4, 3, 2, 3,
3, 2, 1, 2, 4, 3, 2, 3, 4, 3, 2, 3, 3, 2, 1, 2, 2, 1, 0, 1, 3, 2, 1, 2,
5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2, 4, 3, 2, 3, 7, 6, 5, 6, 6, 5, 4, 5,
5, 4, 3, 4, 6, 5, 4, 5, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4,
5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2, 4, 3, 2, 3, 6, 5, 4, 5, 5, 4, 3, 4,
4, 3, 2, 3, 5, 4, 3, 4, 8, 7, 6, 7, 7, 6, 5, 6, 6, 5, 4, 5, 7, 6, 5, 6,
7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 6, 5, 4, 5, 5, 4, 3, 4,
4, 3, 2, 3, 5, 4, 3, 4, 7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5,
12, 11, 10, 11, 11, 10, 9, 10, 10, 9, 8, 9, 11, 10, 9, 10, 11, 10, 9, 10, 10, 9, 8, 9,
9, 8, 7, 8, 10, 9, 8, 9, 10, 9, 8, 9, 9, 8, 7, 8, 8, 7, 6, 7, 9, 8, 7, 8,
11, 10, 9, 10, 10, 9, 8, 9, 9, 8, 7, 8, 10, 9, 8, 9},
{10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 9, 5, 4, 3, 8, 4, 3, 2,
7, 3, 2, 1, 8, 4, 3, 2, 8, 4, 3, 2, 7, 3, 2, 1, 6, 2, 1, 0, 7, 3, 2, 1,
9, 5, 4, 3, 8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2, 11, 7, 6, 5, 10, 6, 5, 4,
9, 5, 4, 3, 10, 6, 5, 4, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3,
9, 5, 4, 3, 8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2, 10, 6, 5, 4, 9, 5, 4, 3,
8, 4, 3, 2, 9, 5, 4, 3, 12, 8, 7, 6, 11, 7, 6, 5, 10, 6, 5, 4, 11, 7, 6, 5,
11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4, 10, 6, 5, 4, 9, 5, 4, 3,
8, 4, 3, 2, 9, 5, 4, 3, 11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4,
16, 12, 11, 10, 15, 11, 10, 9, 14, 10, 9, 8, 15, 11, 10, 9, 15, 11, 10, 9, 14, 10, 9, 8,
13, 9, 8, 7, 14, 10, 9, 8, 14, 10, 9, 8, 13, 9, 8, 7, 12, 8, 7, 6, 13, 9, 8, 7,
15, 11, 10, 9, 14, 10, 9, 8, 13, 9, 8, 7, 14, 10, 9, 8},
{8, 9, 10, 14, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 7, 8, 9, 13, 3, 4, 5, 9,
2, 3, 4, 8, 1, 2, 3, 7, 6, 7, 8, 12, 2, 3, 4, 8, 1, 2, 3, 7, 0, 1, 2, 6,
7, 8, 9, 13, 3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7, 9, 10, 11, 15, 5, 6, 7, 11,
4, 5, 6, 10, 3, 4, 5, 9, 8, 9, 10, 14, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8,
7, 8, 9, 13, 3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7, 8, 9, 10, 14, 4, 5, 6, 10,
3, 4, 5, 9, 2, 3, 4, 8, 10, 11, 12, 16, 6, 7, 8, 12, 5, 6, 7, 11, 4, 5, 6, 10,
9, 10, 11, 15, 5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9, 8, 9, 10, 14, 4, 5, 6, 10,
3, 4, 5, 9, 2, 3, 4, 8, 9, 10, 11, 15, 5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9,
14, 15, 16, 20, 10, 11, 12, 16, 9, 10, 11, 15, 8, 9, 10, 14, 13, 14, 15, 19, 9, 10, 11, 15,
8, 9, 10, 14, 7, 8, 9, 13, 12, 13, 14, 18, 8, 9, 10, 14, 7, 8, 9, 13, 6, 7, 8, 12,
13, 14, 15, 19, 9, 10, 11, 15, 8, 9, 10, 14, 7, 8, 9, 13},
{9, 8, 9, 10, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 8, 7, 8, 9, 4, 3, 4, 5,
3, 2, 3, 4, 2, 1, 2, 3, 7, 6, 7, 8, 3, 2, 3, 4, 2, 1, 2, 3, 1, 0, 1, 2,
8, 7, 8, 9, 4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 10, 9, 10, 11, 6, 5, 6, 7,
5, 4, 5, 6, 4, 3, 4, 5, 9, 8, 9, 10, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4,
8, 7, 8, 9, 4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 9, 8, 9, 10, 5, 4, 5, 6,
4, 3, 4, 5, 3, 2, 3, 4, 11, 10, 11, 12, 7, 6, 7, 8, 6, 5, 6, 7, 5, 4, 5, 6,
10, 9, 10, 11, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 9, 8, 9, 10, 5, 4, 5, 6,
4, 3, 4, 5, 3, 2, 3, 4, 10, 9, 10, 11, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5,
15, 14, 15, 16, 11, 10, 11, 12, 10, 9, 10, 11, 9, 8, 9, 10, 14, 13, 14, 15, 10, 9, 10, 11,
9, 8, 9, 10, 8, 7, 8, 9, 13, 12, 13, 14, 9, 8, 9, 10, 8, 7, 8, 9, 7, 6, 7, 8,
14, 13, 14, 15, 10, 9, 10, 11, 9, 8, 9, 10, 8, 7, 8, 9},
{10, 9, 8, 9, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 9, 8, 7, 8, 5, 4, 3, 4,
4, 3, 2, 3, 3, 2, 1, 2, 8, 7, 6, 7, 4, 3, 2, 3, 3, 2, 1, 2, 2, 1, 0, 1,
9, 8, 7, 8, 5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2, 11, 10, 9, 10, 7, 6, 5, 6,
6, 5, 4, 5, 5, 4, 3, 4, 10, 9, 8, 9, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3,
9, 8, 7, 8, 5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2, 10, 9, 8, 9, 6, 5, 4, 5,
5, 4, 3, 4, 4, 3, 2, 3, 12, 11, 10, 11, 8, 7, 6, 7, 7, 6, 5, 6, 6, 5, 4, 5,
11, 10, 9, 10, 7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4, 10, 9, 8, 9, 6, 5, 4, 5,
5, 4, 3, 4, 4, 3, 2, 3, 11, 10, 9, 10, 7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4,
16, 15, 14, 15, 12, 11, 10, 11, 11, 10, 9, 10, 10, 9, 8, 9, 15, 14, 13, 14, 11, 10, 9, 10,
10, 9, 8, 9, 9, 8, 7, 8, 14, 13, 12, 13, 10, 9, 8, 9, 9, 8, 7, 8, 8, 7, 6, 7,
15, 14, 13, 14, 11, 10, 9, 10, 10, 9, 8, 9, 9, 8, 7, 8},
{14, 10, 9, 8, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 13, 9, 8, 7, 9, 5, 4, 3,
8, 4, 3, 2, 7, 3, 2, 1, 12, 8, 7, 6, 8, 4, 3, 2, 7, 3, 2, 1, 6, 2, 1, 0,
13, 9, 8, 7, 9, 5, 4, 3, 8, 4, 3, 2, 7, 3, 2, 1, 15, 11, 10, 9, 11, 7, 6, 5,
10, 6, 5, 4, 9, 5, 4, 3, 14, 10, 9, 8, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2,
13, 9, 8, 7, 9, 5, 4, 3, 8, 4, 3, 2, 7, 3, 2, 1, 14, 10, 9, 8, 10, 6, 5, 4,
9, 5, 4, 3, 8, 4, 3, 2, 16, 12, 11, 10, 12, 8, 7, 6, 11, 7, 6, 5, 10, 6, 5, 4,
15, 11, 10, 9, 11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3, 14, 10, 9, 8, 10, 6, 5, 4,
9, 5, 4, 3, 8, 4, 3, 2, 15, 11, 10, 9, 11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3,
20, 16, 15, 14, 16, 12, 11, 10, 15, 11, 10, 9, 14, 10, 9, 8, 19, 15, 14, 13, 15, 11, 10, 9,
14, 10, 9, 8, 13, 9, 8, 7, 18, 14, 13, 12, 14, 10, 9, 8, 13, 9, 8, 7, 12, 8, 7, 6,
19, 15, 14, 13, 15, 11, 10, 9, 14, 10, 9, 8, 13, 9, 8, 7},
{6, 7, 8, 12, 7, 8, 9, 13, 8, 9, 10, 14, 12, 13, 14, 18, 2, 3, 4, 8, 3, 4, 5, 9,
4, 5, 6, 10, 8, 9, 10, 14, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 7, 8, 9, 13,
0, 1, 2, 6, 1, 2, 3, 7, 2, 3, 4, 8, 6, 7, 8, 12, 7, 8, 9, 13, 8, 9, 10, 14,
9, 10, 11, 15, 13, 14, 15, 19, 3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11, 9, 10, 11, 15,
2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14, 1, 2, 3, 7, 2, 3, 4, 8,
3, 4, 5, 9, 7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15, 10, 11, 12, 16, 14, 15, 16, 20,
4, 5, 6, 10, 5, 6, 7, 11, 6, 7, 8, 12, 10, 11, 12, 16, 3, 4, 5, 9, 4, 5, 6, 10,
5, 6, 7, 11, 9, 10, 11, 15, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14,
12, 13, 14, 18, 13, 14, 15, 19, 14, 15, 16, 20, 18, 19, 20, 24, 8, 9, 10, 14, 9, 10, 11, 15,
10, 11, 12, 16, 14, 15, 16, 20, 7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15, 13, 14, 15, 19,
6, 7, 8, 12, 7, 8, 9, 13, 8, 9, 10, 14, 12, 13, 14, 18},
{7, 6, 7, 8, 8, 7, 8, 9, 9, 8, 9, 10, 13, 12, 13, 14, 3, 2, 3, 4, 4, 3, 4, 5,
5, 4, 5, 6, 9, 8, 9, 10, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 8, 7, 8, 9,
1, 0, 1, 2, 2, 1, 2, 3, 3, 2, 3, 4, 7, 6, 7, 8, 8, 7, 8, 9, 9, 8, 9, 10,
10, 9, 10, 11, 14, 13, 14, 15, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 10, 9, 10, 11,
3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10, 2, 1, 2, 3, 3, 2, 3, 4,
4, 3, 4, 5, 8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11, 11, 10, 11, 12, 15, 14, 15, 16,
5, 4, 5, 6, 6, 5, 6, 7, 7, 6, 7, 8, 11, 10, 11, 12, 4, 3, 4, 5, 5, 4, 5, 6,
6, 5, 6, 7, 10, 9, 10, 11, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10,
13, 12, 13, 14, 14, 13, 14, 15, 15, 14, 15, 16, 19, 18, 19, 20, 9, 8, 9, 10, 10, 9, 10, 11,
11, 10, 11, 12, 15, 14, 15, 16, 8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11, 14, 13, 14, 15,
7, 6, 7, 8, 8, 7, 8, 9, 9, 8, 9, 10, 13, 12, 13, 14},
{8, 7, 6, 7, 9, 8, 7, 8, 10, 9, 8, 9, 14, 13, 12, 13, 4, 3, 2, 3, 5, 4, 3, 4,
6, 5, 4, 5, 10, 9, 8, 9, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 9, 8, 7, 8,
2, 1, 0, 1, 3, 2, 1, 2, 4, 3, 2, 3, 8, 7, 6, 7, 9, 8, 7, 8, 10, 9, 8, 9,
11, 10, 9, 10, 15, 14, 13, 14, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 11, 10, 9, 10,
4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9, 3, 2, 1, 2, 4, 3, 2, 3,
5, 4, 3, 4, 9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10, 12, 11, 10, 11, 16, 15, 14, 15,
6, 5, 4, 5, 7, 6, 5, 6, 8, 7, 6, 7, 12, 11, 10, 11, 5, 4, 3, 4, 6, 5, 4, 5,
7, 6, 5, 6, 11, 10, 9, 10, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9,
14, 13, 12, 13, 15, 14, 13, 14, 16, 15, 14, 15, 20, 19, 18, 19, 10, 9, 8, 9, 11, 10, 9, 10,
12, 11, 10, 11, 16, 15, 14, 15, 9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10, 15, 14, 13, 14,
8, 7, 6, 7, 9, 8, 7, 8, 10, 9, 8, 9, 14, 13, 12, 13},
{12, 8, 7, 6, 13, 9, 8, 7, 14, 10, 9, 8, 18, 14, 13, 12, 8, 4, 3, 2, 9, 5, 4, 3,
10, 6, 5, 4, 14, 10, 9, 8, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 13, 9, 8, 7,
6, 2, 1, 0, 7, 3, 2, 1, 8, 4, 3, 2, 12, 8, 7, 6, 13, 9, 8, 7, 14, 10, 9, 8,
15, 11, 10, 9, 19, 15, 14, 13, 9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5, 15, 11, 10, 9,
8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8, 7, 3, 2, 1, 8, 4, 3, 2,
9, 5, 4, 3, 13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9, 16, 12, 11, 10, 20, 16, 15, 14,
10, 6, 5, 4, 11, 7, 6, 5, 12, 8, 7, 6, 16, 12, 11, 10, 9, 5, 4, 3, 10, 6, 5, 4,
11, 7, 6, 5, 15, 11, 10, 9, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8,
18, 14, 13, 12, 19, 15, 14, 13, 20, 16, 15, 14, 24, 20, 19, 18, 14, 10, 9, 8, 15, 11, 10, 9,
16, 12, 11, 10, 20, 16, 15, 14, 13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9, 19, 15, 14, 13,
12, 8, 7, 6, 13, 9, 8, 7, 14, 10, 9, 8, 18, 14, 13, 12},
{7, 8, 9, 13, 6, 7, 8, 12, 7, 8, 9, 13, 8, 9, 10, 14, 3, 4, 5, 9, 2, 3, 4, 8,
3, 4, 5, 9, 4, 5, 6, 10, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9,
1, 2, 3, 7, 0, 1, 2, 6, 1, 2, 3, 7, 2, 3, 4, 8, 8, 9, 10, 14, 7, 8, 9, 13,
8, 9, 10, 14, 9, 10, 11, 15, 4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11,
3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 2, 3, 4, 8, 1, 2, 3, 7,
2, 3, 4, 8, 3, 4, 5, 9, 9, 10, 11, 15, 8, 9, 10, 14, 9, 10, 11, 15, 10, 11, 12, 16,
5, 6, 7, 11, 4, 5, 6, 10, 5, 6, 7, 11, 6, 7, 8, 12, 4, 5, 6, 10, 3, 4, 5, 9,
4, 5, 6, 10, 5, 6, 7, 11, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10,
13, 14, 15, 19, 12, 13, 14, 18, 13, 14, 15, 19, 14, 15, 16, 20, 9, 10, 11, 15, 8, 9, 10, 14,
9, 10, 11, 15, 10, 11, 12, 16, 8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15,
7, 8, 9, 13, 6, 7, 8, 12, 7, 8, 9, 13, 8, 9, 10, 14},
{8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9, 9, 8, 9, 10, 4, 3, 4, 5, 3, 2, 3, 4,
4, 3, 4, 5, 5, 4, 5, 6, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5,
2, 1, 2, 3, 1, 0, 1, 2, 2, 1, 2, 3, 3, 2, 3, 4, 9, 8, 9, 10, 8, 7, 8, 9,
9, 8, 9, 10, 10, 9, 10, 11, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7,
4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 3, 2, 3, 4, 2, 1, 2, 3,
3, 2, 3, 4, 4, 3, 4, 5, 10, 9, 10, 11, 9, 8, 9, 10, 10, 9, 10, 11, 11, 10, 11, 12,
6, 5, 6, 7, 5, 4, 5, 6, 6, 5, 6, 7, 7, 6, 7, 8, 5, 4, 5, 6, 4, 3, 4, 5,
5, 4, 5, 6, 6, 5, 6, 7, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6,
14, 13, 14, 15, 13, 12, 13, 14, 14, 13, 14, 15, 15, 14, 15, 16, 10, 9, 10, 11, 9, 8, 9, 10,
10, 9, 10, 11, 11, 10, 11, 12, 9, 8, 9, 10, 8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11,
8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9, 9, 8, 9, 10},
{9, 8, 7, 8, 8, 7, 6, 7, 9, 8, 7, 8, 10, 9, 8, 9, 5, 4, 3, 4, 4, 3, 2, 3,
5, 4, 3, 4, 6, 5, 4, 5, 4, 3, 2, 3, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4,
3, 2, 1, 2, 2, 1, 0, 1, 3, 2, 1, 2, 4, 3, 2, 3, 10, 9, 8, 9, 9, 8, 7, 8,
10, 9, 8, 9, 11, 10, 9, 10, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6,
5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 4, 3, 2, 3, 3, 2, 1, 2,
4, 3, 2, 3, 5, 4, 3, 4, 11, 10, 9, 10, 10, 9, 8, 9, 11, 10, 9, 10, 12, 11, 10, 11,
7, 6, 5, 6, 6, 5, 4, 5, 7, 6, 5, 6, 8, 7, 6, 7, 6, 5, 4, 5, 5, 4, 3, 4,
6, 5, 4, 5, 7, 6, 5, 6, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5,
15, 14, 13, 14, 14, 13, 12, 13, 15, 14, 13, 14, 16, 15, 14, 15, 11, 10, 9, 10, 10, 9, 8, 9,
11, 10, 9, 10, 12, 11, 10, 11, 10, 9, 8, 9, 9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10,
9, 8, 7, 8, 8, 7, 6, 7, 9, 8, 7, 8, 10, 9, 8, 9},
{13, 9, 8, 7, 12, 8, 7, 6, 13, 9, 8, 7, 14, 10, 9, 8, 9, 5, 4, 3, 8, 4, 3, 2,
9, 5, 4, 3, 10, 6, 5, 4, 8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3,
7, 3, 2, 1, 6, 2, 1, 0, 7, 3, 2, 1, 8, 4, 3, 2, 14, 10, 9, 8, 13, 9, 8, 7,
14, 10, 9, 8, 15, 11, 10, 9, 10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5,
9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 8, 4, 3, 2, 7, 3, 2, 1,
8, 4, 3, 2, 9, 5, 4, 3, 15, 11, 10, 9, 14, 10, 9, 8, 15, 11, 10, 9, 16, 12, 11, 10,
11, 7, 6, 5, 10, 6, 5, 4, 11, 7, 6, 5, 12, 8, 7, 6, 10, 6, 5, 4, 9, 5, 4, 3,
10, 6, 5, 4, 11, 7, 6, 5, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4,
19, 15, 14, 13, 18, 14, 13, 12, 19, 15, 14, 13, 20, 16, 15, 14, 15, 11, 10, 9, 14, 10, 9, 8,
15, 11, 10, 9, 16, 12, 11, 10, 14, 10, 9, 8, 13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9,
13, 9, 8, 7, 12, 8, 7, 6, 13, 9, 8, 7, 14, 10, 9, 8},
{8, 9, 10, 14, 7, 8, 9, 13, 6, 7, 8, 12, 7, 8, 9, 13, 4, 5, 6, 10, 3, 4, 5, 9,
2, 3, 4, 8, 3, 4, 5, 9, 3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8,
2, 3, 4, 8, 1, 2, 3, 7, 0, 1, 2, 6, 1, 2, 3, 7, 9, 10, 11, 15, 8, 9, 10, 14,
7, 8, 9, 13, 8, 9, 10, 14, 5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10,
4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 3, 4, 5, 9, 2, 3, 4, 8,
1, 2, 3, 7, 2, 3, 4, 8, 10, 11, 12, 16, 9, 10, 11, 15, 8, 9, 10, 14, 9, 10, 11, 15,
6, 7, 8, 12, 5, 6, 7, 11, 4, 5, 6, 10, 5, 6, 7, 11, 5, 6, 7, 11, 4, 5, 6, 10,
3, 4, 5, 9, 4, 5, 6, 10, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9,
14, 15, 16, 20, 13, 14, 15, 19, 12, 13, 14, 18, 13, 14, 15, 19, 10, 11, 12, 16, 9, 10, 11, 15,
8, 9, 10, 14, 9, 10, 11, 15, 9, 10, 11, 15, 8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14,
8, 9, 10, 14, 7, 8, 9, 13, 6, 7, 8, 12, 7, 8, 9, 13},
{9, 8, 9, 10, 8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9, 5, 4, 5, 6, 4, 3, 4, 5,
3, 2, 3, 4, 4, 3, 4, 5, 4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4,
3, 2, 3, 4, 2, 1, 2, 3, 1, 0, 1, 2, 2, 1, 2, 3, 10, 9, 10, 11, 9, 8, 9, 10,
8, 7, 8, 9, 9, 8, 9, 10, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6,
5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 4, 3, 4, 5, 3, 2, 3, 4,
2, 1, 2, 3, 3, 2, 3, 4, 11, 10, 11, 12, 10, 9, 10, 11, 9, 8, 9, 10, 10, 9, 10, 11,
7, 6, 7, 8, 6, 5, 6, 7, 5, 4, 5, 6, 6, 5, 6, 7, 6, 5, 6, 7, 5, 4, 5, 6,
4, 3, 4, 5, 5, 4, 5, 6, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5,
15, 14, 15, 16, 14, 13, 14, 15, 13, 12, 13, 14, 14, 13, 14, 15, 11, 10, 11, 12, 10, 9, 10, 11,
9, 8, 9, 10, 10, 9, 10, 11, 10, 9, 10, 11, 9, 8, 9, 10, 8, 7, 8, 9, 9, 8, 9, 10,
9, 8, 9, 10, 8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9},
{10, 9, 8, 9, 9, 8, 7, 8, 8, 7, 6, 7, 9, 8, 7, 8, 6, 5, 4, 5, 5, 4, 3, 4,
4, 3, 2, 3, 5, 4, 3, 4, 5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2, 4, 3, 2, 3,
4, 3, 2, 3, 3, 2, 1, 2, 2, 1, 0, 1, 3, 2, 1, 2, 11, 10, 9, 10, 10, 9, 8, 9,
9, 8, 7, 8, 10, 9, 8, 9, 7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5,
6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 5, 4, 3, 4, 4, 3, 2, 3,
3, 2, 1, 2, 4, 3, 2, 3, 12, 11, 10, 11, 11, 10, 9, 10, 10, 9, 8, 9, 11, 10, 9, 10,
8, 7, 6, 7, 7, 6, 5, 6, 6, 5, 4, 5, 7, 6, 5, 6, 7, 6, 5, 6, 6, 5, 4, 5,
5, 4, 3, 4, 6, 5, 4, 5, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4,
16, 15, 14, 15, 15, 14, 13, 14, 14, 13, 12, 13, 15, 14, 13, 14, 12, 11, 10, 11, 11, 10, 9, 10,
10, 9, 8, 9, 11, 10, 9, 10, 11, 10, 9, 10, 10, 9, 8, 9, 9, 8, 7, 8, 10, 9, 8, 9,
10, 9, 8, 9, 9, 8, 7, 8, 8, 7, 6, 7, 9, 8, 7, 8},
{14, 10, 9, 8, 13, 9, 8, 7, 12, 8, 7, 6, 13, 9, 8, 7, 10, 6, 5, 4, 9, 5, 4, 3,
8, 4, 3, 2, 9, 5, 4, 3, 9, 5, 4, 3, 8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2,
8, 4, 3, 2, 7, 3, 2, 1, 6, 2, 1, 0, 7, 3, 2, 1, 15, 11, 10, 9, 14, 10, 9, 8,
13, 9, 8, 7, 14, 10, 9, 8, 11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4,
10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 9, 5, 4, 3, 8, 4, 3, 2,
7, 3, 2, 1, 8, 4, 3, 2, 16, 12, 11, 10, 15, 11, 10, 9, 14, 10, 9, 8, 15, 11, 10, 9,
12, 8, 7, 6, 11, 7, 6, 5, 10, 6, 5, 4, 11, 7, 6, 5, 11, 7, 6, 5, 10, 6, 5, 4,
9, 5, 4, 3, 10, 6, 5, 4, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3,
20, 16, 15, 14, 19, 15, 14, 13, 18, 14, 13, 12, 19, 15, 14, 13, 16, 12, 11, 10, 15, 11, 10, 9,
14, 10, 9, 8, 15, 11, 10, 9, 15, 11, 10, 9, 14, 10, 9, 8, 13, 9, 8, 7, 14, 10, 9, 8,
14, 10, 9, 8, 13, 9, 8, 7, 12, 8, 7, 6, 13, 9, 8, 7},
{12, 13, 14, 18, 8, 9, 10, 14, 7, 8, 9, 13, 6, 7, 8, 12, 8, 9, 10, 14, 4, 5, 6, 10,
3, 4, 5, 9, 2, 3, 4, 8, 7, 8, 9, 13, 3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7,
6, 7, 8, 12, 2, 3, 4, 8, 1, 2, 3, 7, 0, 1, 2, 6, 13, 14, 15, 19, 9, 10, 11, 15,
8, 9, 10, 14, 7, 8, 9, 13, 9, 10, 11, 15, 5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9,
8, 9, 10, 14, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 7, 8, 9, 13, 3, 4, 5, 9,
2, 3, 4, 8, 1, 2, 3, 7, 14, 15, 16, 20, 10, 11, 12, 16, 9, 10, 11, 15, 8, 9, 10, 14,
10, 11, 12, 16, 6, 7, 8, 12, 5, 6, 7, 11, 4, 5, 6, 10, 9, 10, 11, 15, 5, 6, 7, 11,
4, 5, 6, 10, 3, 4, 5, 9, 8, 9, 10, 14, 4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8,
18, 19, 20, 24, 14, 15, 16, 20, 13, 14, 15, 19, 12, 13, 14, 18, 14, 15, 16, 20, 10, 11, 12, 16,
9, 10, 11, 15, 8, 9, 10, 14, 13, 14, 15, 19, 9, 10, 11, 15, 8, 9, 10, 14, 7, 8, 9, 13,
12, 13, 14, 18, 8, 9, 10, 14, 7, 8, 9, 13, 6, 7, 8, 12},
{13, 12, 13, 14, 9, 8, 9, 10, 8, 7, 8, 9, 7, 6, 7, 8, 9, 8, 9, 10, 5, 4, 5, 6,
4, 3, 4, 5, 3, 2, 3, 4, 8, 7, 8, 9, 4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3,
7, 6, 7, 8, 3, 2, 3, 4, 2, 1, 2, 3, 1, 0, 1, 2, 14, 13, 14, 15, 10, 9, 10, 11,
9, 8, 9, 10, 8, 7, 8, 9, 10, 9, 10, 11, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5,
9, 8, 9, 10, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4, 8, 7, 8, 9, 4, 3, 4, 5,
3, 2, 3, 4, 2, 1, 2, 3, 15, 14, 15, 16, 11, 10, 11, 12, 10, 9, 10, 11, 9, 8, 9, 10,
11, 10, 11, 12, 7, 6, 7, 8, 6, 5, 6, 7, 5, 4, 5, 6, 10, 9, 10, 11, 6, 5, 6, 7,
5, 4, 5, 6, 4, 3, 4, 5, 9, 8, 9, 10, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4,
19, 18, 19, 20, 15, 14, 15, 16, 14, 13, 14, 15, 13, 12, 13, 14, 15, 14, 15, 16, 11, 10, 11, 12,
10, 9, 10, 11, 9, 8, 9, 10, 14, 13, 14, 15, 10, 9, 10, 11, 9, 8, 9, 10, 8, 7, 8, 9,
13, 12, 13, 14, 9, 8, 9, 10, 8, 7, 8, 9, 7, 6, 7, 8},
{14, 13, 12, 13, 10, 9, 8, 9, 9, 8, 7, 8, 8, 7, 6, 7, 10, 9, 8, 9, 6, 5, 4, 5,
5, 4, 3, 4, 4, 3, 2, 3, 9, 8, 7, 8, 5, 4, 3, 4, 4, 3, 2, 3, 3, 2, 1, 2,
8, 7, 6, 7, 4, 3, 2, 3, 3, 2, 1, 2, 2, 1, 0, 1, 15, 14, 13, 14, 11, 10, 9, 10,
10, 9, 8, 9, 9, 8, 7, 8, 11, 10, 9, 10, 7, 6, 5, 6, 6, 5, 4, 5, 5, 4, 3, 4,
10, 9, 8, 9, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 9, 8, 7, 8, 5, 4, 3, 4,
4, 3, 2, 3, 3, 2, 1, 2, 16, 15, 14, 15, 12, 11, 10, 11, 11, 10, 9, 10, 10, 9, 8, 9,
12, 11, 10, 11, 8, 7, 6, 7, 7, 6, 5, 6, 6, 5, 4, 5, 11, 10, 9, 10, 7, 6, 5, 6,
6, 5, 4, 5, 5, 4, 3, 4, 10, 9, 8, 9, 6, 5, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3,
20, 19, 18, 19, 16, 15, 14, 15, 15, 14, 13, 14, 14, 13, 12, 13, 16, 15, 14, 15, 12, 11, 10, 11,
11, 10, 9, 10, 10, 9, 8, 9, 15, 14, 13, 14, 11, 10, 9, 10, 10, 9, 8, 9, 9, 8, 7, 8,
14, 13, 12, 13, 10, 9, 8, 9, 9, 8, 7, 8, 8, 7, 6, 7},
{18, 14, 13, 12, 14, 10, 9, 8, 13, 9, 8, 7, 12, 8, 7, 6, 14, 10, 9, 8, 10, 6, 5, 4,
9, 5, 4, 3, 8, 4, 3, 2, 13, 9, 8, 7, 9, 5, 4, 3, 8, 4, 3, 2, 7, 3, 2, 1,
12, 8, 7, 6, 8, 4, 3, 2, 7, 3, 2, 1, 6, 2, 1, 0, 19, 15, 14, 13, 15, 11, 10, 9,
14, 10, 9, 8, 13, 9, 8, 7, 15, 11, 10, 9, 11, 7, 6, 5, 10, 6, 5, 4, 9, 5, 4, 3,
14, 10, 9, 8, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2, 13, 9, 8, 7, 9, 5, 4, 3,
8, 4, 3, 2, 7, 3, 2, 1, 20, 16, 15, 14, 16, 12, 11, 10, 15, 11, 10, 9, 14, 10, 9, 8,
16, 12, 11, 10, 12, 8, 7, 6, 11, 7, 6, 5, 10, 6, 5, 4, 15, 11, 10, 9, 11, 7, 6, 5,
10, 6, 5, 4, 9, 5, 4, 3, 14, 10, 9, 8, 10, 6, 5, 4, 9, 5, 4, 3, 8, 4, 3, 2,
24, 20, 19, 18, 20, 16, 15, 14, 19, 15, 14, 13, 18, 14, 13, 12, 20, 16, 15, 14, 16, 12, 11, 10,
15, 11, 10, 9, 14, 10, 9, 8, 19, 15, 14, 13, 15, 11, 10, 9, 14, 10, 9, 8, 13, 9, 8, 7,
18, 14, 13, 12, 14, 10, 9, 8, 13, 9, 8, 7, 12, 8, 7, 6},
{1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 7, 8, 9, 13, 2, 3, 4, 8, 3, 4, 5, 9,
4, 5, 6, 10, 8, 9, 10, 14, 3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11, 9, 10, 11, 15,
7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15, 13, 14, 15, 19, 0, 1, 2, 6, 1, 2, 3, 7,
2, 3, 4, 8, 6, 7, 8, 12, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 7, 8, 9, 13,
2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14, 6, 7, 8, 12, 7, 8, 9, 13,
8, 9, 10, 14, 12, 13, 14, 18, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 7, 8, 9, 13,
2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14, 3, 4, 5, 9, 4, 5, 6, 10,
5, 6, 7, 11, 9, 10, 11, 15, 7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15, 13, 14, 15, 19,
2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 8, 9, 10, 14, 3, 4, 5, 9, 4, 5, 6, 10,
5, 6, 7, 11, 9, 10, 11, 15, 4, 5, 6, 10, 5, 6, 7, 11, 6, 7, 8, 12, 10, 11, 12, 16,
8, 9, 10, 14, 9, 10, 11, 15, 10, 11, 12, 16, 14, 15, 16, 20},
{2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 8, 7, 8, 9, 3, 2, 3, 4, 4, 3, 4, 5,
5, 4, 5, 6, 9, 8, 9, 10, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 10, 9, 10, 11,
8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11, 14, 13, 14, 15, 1, 0, 1, 2, 2, 1, 2, 3,
3, 2, 3, 4, 7, 6, 7, 8, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 8, 7, 8, 9,
3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10, 7, 6, 7, 8, 8, 7, 8, 9,
9, 8, 9, 10, 13, 12, 13, 14, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 8, 7, 8, 9,
3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10, 4, 3, 4, 5, 5, 4, 5, 6,
6, 5, 6, 7, 10, 9, 10, 11, 8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11, 14, 13, 14, 15,
3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6, 9, 8, 9, 10, 4, 3, 4, 5, 5, 4, 5, 6,
6, 5, 6, 7, 10, 9, 10, 11, 5, 4, 5, 6, 6, 5, 6, 7, 7, 6, 7, 8, 11, 10, 11, 12,
9, 8, 9, 10, 10, 9, 10, 11, 11, 10, 11, 12, 15, 14, 15, 16},
{3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 9, 8, 7, 8, 4, 3, 2, 3, 5, 4, 3, 4,
6, 5, 4, 5, 10, 9, 8, 9, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 11, 10, 9, 10,
9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10, 15, 14, 13, 14, 2, 1, 0, 1, 3, 2, 1, 2,
4, 3, 2, 3, 8, 7, 6, 7, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 9, 8, 7, 8,
4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9, 8, 7, 6, 7, 9, 8, 7, 8,
10, 9, 8, 9, 14, 13, 12, 13, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 9, 8, 7, 8,
4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9, 5, 4, 3, 4, 6, 5, 4, 5,
7, 6, 5, 6, 11, 10, 9, 10, 9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10, 15, 14, 13, 14,
4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5, 10, 9, 8, 9, 5, 4, 3, 4, 6, 5, 4, 5,
7, 6, 5, 6, 11, 10, 9, 10, 6, 5, 4, 5, 7, 6, 5, 6, 8, 7, 6, 7, 12, 11, 10, 11,
10, 9, 8, 9, 11, 10, 9, 10, 12, 11, 10, 11, 16, 15, 14, 15},
{7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 13, 9, 8, 7, 8, 4, 3, 2, 9, 5, 4, 3,
10, 6, 5, 4, 14, 10, 9, 8, 9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5, 15, 11, 10, 9,
13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9, 19, 15, 14, 13, 6, 2, 1, 0, 7, 3, 2, 1,
8, 4, 3, 2, 12, 8, 7, 6, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 13, 9, 8, 7,
8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8, 12, 8, 7, 6, 13, 9, 8, 7,
14, 10, 9, 8, 18, 14, 13, 12, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 13, 9, 8, 7,
8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8, 9, 5, 4, 3, 10, 6, 5, 4,
11, 7, 6, 5, 15, 11, 10, 9, 13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9, 19, 15, 14, 13,
8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 14, 10, 9, 8, 9, 5, 4, 3, 10, 6, 5, 4,
11, 7, 6, 5, 15, 11, 10, 9, 10, 6, 5, 4, 11, 7, 6, 5, 12, 8, 7, 6, 16, 12, 11, 10,
14, 10, 9, 8, 15, 11, 10, 9, 16, 12, 11, 10, 20, 16, 15, 14},
{2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9, 3, 4, 5, 9, 2, 3, 4, 8,
3, 4, 5, 9, 4, 5, 6, 10, 4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10, 5, 6, 7, 11,
8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15, 1, 2, 3, 7, 0, 1, 2, 6,
1, 2, 3, 7, 2, 3, 4, 8, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9,
3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 7, 8, 9, 13, 6, 7, 8, 12,
7, 8, 9, 13, 8, 9, 10, 14, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 3, 4, 5, 9,
3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 4, 5, 6, 10, 3, 4, 5, 9,
4, 5, 6, 10, 5, 6, 7, 11, 8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14, 9, 10, 11, 15,
3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 4, 5, 6, 10, 4, 5, 6, 10, 3, 4, 5, 9,
4, 5, 6, 10, 5, 6, 7, 11, 5, 6, 7, 11, 4, 5, 6, 10, 5, 6, 7, 11, 6, 7, 8, 12,
9, 10, 11, 15, 8, 9, 10, 14, 9, 10, 11, 15, 10, 11, 12, 16},
{3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3,
4, 5, 5, 4, 5, 6, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 9, 8, 9, 10,
8, 7, 8, 9, 9, 8, 9, 10, 10, 9, 10, 11, 2, 1, 2, 3, 1, 0, 1, 2, 2, 1, 2, 3, 3, 2,
3, 4, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 4, 3, 4, 5, 3, 2, 3, 4,
4, 3, 4, 5, 5, 4, 5, 6, 8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9, 9, 8, 9, 10, 3, 2,
3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 5, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5,
5, 4, 5, 6, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 9, 8, 9, 10, 8, 7,
8, 9, 9, 8, 9, 10, 10, 9, 10, 11, 4, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 5, 6,
5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 6, 7, 6, 5, 6, 7, 5, 4, 5, 6, 6, 5,
6, 7, 7, 6, 7, 8, 10, 9, 10, 11, 9, 8, 9, 10, 10, 9, 10, 11, 11, 10, 11, 12},
{4, 3, 2, 3, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4,
3, 4, 6, 5, 4, 5, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 10, 9, 8, 9,
9, 8, 7, 8, 10, 9, 8, 9, 11, 10, 9, 10, 3, 2, 1, 2, 2, 1, 0, 1, 3, 2, 1, 2, 4, 3,
2, 3, 4, 3, 2, 3, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 5, 4, 3, 4, 4, 3, 2, 3,
5, 4, 3, 4, 6, 5, 4, 5, 9, 8, 7, 8, 8, 7, 6, 7, 9, 8, 7, 8, 10, 9, 8, 9, 4, 3,
2, 3, 3, 2, 1, 2, 4, 3, 2, 3, 5, 4, 3, 4, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4,
6, 5, 4, 5, 6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 10, 9, 8, 9, 9, 8,
7, 8, 10, 9, 8, 9, 11, 10, 9, 10, 5, 4, 3, 4, 4, 3, 2, 3, 5, 4, 3, 4, 6, 5, 4, 5,
6, 5, 4, 5, 5, 4, 3, 4, 6, 5, 4, 5, 7, 6, 5, 6, 7, 6, 5, 6, 6, 5, 4, 5, 7, 6,
5, 6, 8, 7, 6, 7, 11, 10, 9, 10, 10, 9, 8, 9, 11, 10, 9, 10, 12, 11, 10, 11},
{8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3, 9, 5, 4, 3, 8, 4, 3, 2,
9, 5, 4, 3, 10, 6, 5, 4, 10, 6, 5, 4, 9, 5, 4, 3, 10, 6, 5, 4, 11, 7, 6, 5,
14, 10, 9, 8, 13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9, 7, 3, 2, 1, 6, 2, 1, 0,
7, 3, 2, 1, 8, 4, 3, 2, 8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3,
9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 13, 9, 8, 7, 12, 8, 7, 6,
13, 9, 8, 7, 14, 10, 9, 8, 8, 4, 3, 2, 7, 3, 2, 1, 8, 4, 3, 2, 9, 5, 4, 3,
9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 10, 6, 5, 4, 9, 5, 4, 3,
10, 6, 5, 4, 11, 7, 6, 5, 14, 10, 9, 8, 13, 9, 8, 7, 14, 10, 9, 8, 15, 11, 10, 9,
9, 5, 4, 3, 8, 4, 3, 2, 9, 5, 4, 3, 10, 6, 5, 4, 10, 6, 5, 4, 9, 5, 4, 3,
10, 6, 5, 4, 11, 7, 6, 5, 11, 7, 6, 5, 10, 6, 5, 4, 11, 7, 6, 5, 12, 8, 7, 6,
15, 11, 10, 9, 14, 10, 9, 8, 15, 11, 10, 9, 16, 12, 11, 10},
{3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8, 4, 5, 6, 10, 3, 4, 5, 9,
2, 3, 4, 8, 3, 4, 5, 9, 5, 6, 7, 11, 4, 5, 6, 10, 3, 4, 5, 9, 4, 5, 6, 10,
9, 10, 11, 15, 8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14, 2, 3, 4, 8, 1, 2, 3, 7,
0, 1, 2, 6, 1, 2, 3, 7, 3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8,
4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 8, 9, 10, 14, 7, 8, 9, 13,
6, 7, 8, 12, 7, 8, 9, 13, 3, 4, 5, 9, 2, 3, 4, 8, 1, 2, 3, 7, 2, 3, 4, 8,
4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 5, 6, 7, 11, 4, 5, 6, 10,
3, 4, 5, 9, 4, 5, 6, 10, 9, 10, 11, 15, 8, 9, 10, 14, 7, 8, 9, 13, 8, 9, 10, 14,
4, 5, 6, 10, 3, 4, 5, 9, 2, 3, 4, 8, 3, 4, 5, 9, 5, 6, 7, 11, 4, 5, 6, 10,
3, 4, 5, 9, 4, 5, 6, 10, 6, 7, 8, 12, 5, 6, 7, 11, 4, 5, 6, 10, 5, 6, 7, 11,
10, 11, 12, 16, 9, 10, 11, 15, 8, 9, 10, 14, 9, 10, 11, 15},
{4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2,
3, 4, 4, 3, 4, 5, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 10, 9, 10, 11,
9, 8, 9, 10, 8, 7, 8, 9, 9, 8, 9, 10, 3, 2, 3, 4, 2, 1, 2, 3, 1, 0, 1, 2, 2, 1,
2, 3, 4, 3, 4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 5, 4, 5, 6, 4, 3, 4, 5,
3, 2, 3, 4, 4, 3, 4, 5, 9, 8, 9, 10, 8, 7, 8, 9, 7, 6, 7, 8, 8, 7, 8, 9, 4, 3,
4, 5, 3, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 5, 4, 5, 6, 4, 3, 4, 5, 3, 2, 3, 4,
4, 3, 4, 5, 6, 5, 6, 7, 5, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 10, 9, 10, 11, 9, 8,