forked from OSchip/llvm-project
561 lines
13 KiB
C++
561 lines
13 KiB
C++
//===-------------------------- hash.cpp ----------------------------------===//
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//
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// The LLVM Compiler Infrastructure
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//
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// This file is dual licensed under the MIT and the University of Illinois Open
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// Source Licenses. See LICENSE.TXT for details.
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//
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//===----------------------------------------------------------------------===//
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#include "__hash_table"
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#include "algorithm"
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#include "stdexcept"
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_LIBCPP_BEGIN_NAMESPACE_STD
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namespace {
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// handle all next_prime(i) for i in [1, 210), special case 0
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const unsigned small_primes[] =
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{
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0,
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2,
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3,
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5,
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7,
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11,
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13,
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17,
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19,
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23,
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29,
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31,
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37,
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41,
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43,
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47,
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53,
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59,
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61,
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67,
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71,
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73,
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79,
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83,
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89,
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97,
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101,
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103,
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107,
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109,
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113,
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127,
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131,
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137,
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139,
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149,
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151,
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157,
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163,
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167,
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173,
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179,
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181,
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191,
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193,
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197,
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199,
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211
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};
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// potential primes = 210*k + indices[i], k >= 1
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// these numbers are not divisible by 2, 3, 5 or 7
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// (or any integer 2 <= j <= 10 for that matter).
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const unsigned indices[] =
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{
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1,
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11,
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13,
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17,
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19,
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23,
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29,
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31,
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37,
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41,
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43,
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47,
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53,
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59,
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61,
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67,
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71,
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73,
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79,
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83,
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89,
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97,
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101,
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103,
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107,
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109,
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113,
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121,
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127,
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131,
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137,
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139,
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143,
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149,
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151,
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157,
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163,
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167,
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169,
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173,
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179,
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181,
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187,
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191,
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193,
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197,
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199,
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209
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};
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}
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// Returns: If n == 0, returns 0. Else returns the lowest prime number that
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// is greater than or equal to n.
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//
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// The algorithm creates a list of small primes, plus an open-ended list of
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// potential primes. All prime numbers are potential prime numbers. However
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// some potential prime numbers are not prime. In an ideal world, all potential
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// prime numbers would be prime. Candiate prime numbers are chosen as the next
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// highest potential prime. Then this number is tested for prime by dividing it
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// by all potential prime numbers less than the sqrt of the candidate.
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//
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// This implementation defines potential primes as those numbers not divisible
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// by 2, 3, 5, and 7. Other (common) implementations define potential primes
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// as those not divisible by 2. A few other implementations define potential
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// primes as those not divisible by 2 or 3. By raising the number of small
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// primes which the potential prime is not divisible by, the set of potential
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// primes more closely approximates the set of prime numbers. And thus there
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// are fewer potential primes to search, and fewer potential primes to divide
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// against.
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inline _LIBCPP_INLINE_VISIBILITY
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void
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__check_for_overflow(size_t N, integral_constant<size_t, 32>)
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{
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#ifndef _LIBCPP_NO_EXCEPTIONS
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if (N > 0xFFFFFFFB)
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throw overflow_error("__next_prime overflow");
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#endif
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}
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inline _LIBCPP_INLINE_VISIBILITY
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void
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__check_for_overflow(size_t N, integral_constant<size_t, 64>)
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{
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#ifndef _LIBCPP_NO_EXCEPTIONS
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if (N > 0xFFFFFFFFFFFFFFC5ull)
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throw overflow_error("__next_prime overflow");
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#endif
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}
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size_t
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__next_prime(size_t n)
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{
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const size_t L = 210;
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const size_t N = sizeof(small_primes) / sizeof(small_primes[0]);
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// If n is small enough, search in small_primes
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if (n <= small_primes[N-1])
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return *std::lower_bound(small_primes, small_primes + N, n);
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// Else n > largest small_primes
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// Check for overflow
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__check_for_overflow(n, integral_constant<size_t,
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sizeof(n) * __CHAR_BIT__>());
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// Start searching list of potential primes: L * k0 + indices[in]
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const size_t M = sizeof(indices) / sizeof(indices[0]);
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// Select first potential prime >= n
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// Known a-priori n >= L
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size_t k0 = n / L;
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size_t in = static_cast<size_t>(std::lower_bound(indices, indices + M, n - k0 * L)
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- indices);
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n = L * k0 + indices[in];
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while (true)
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{
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// Divide n by all primes or potential primes (i) until:
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// 1. The division is even, so try next potential prime.
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// 2. The i > sqrt(n), in which case n is prime.
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// It is known a-priori that n is not divisible by 2, 3, 5 or 7,
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// so don't test those (j == 5 -> divide by 11 first). And the
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// potential primes start with 211, so don't test against the last
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// small prime.
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for (size_t j = 5; j < N - 1; ++j)
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{
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const std::size_t p = small_primes[j];
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const std::size_t q = n / p;
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if (q < p)
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return n;
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if (n == q * p)
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goto next;
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}
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// n wasn't divisible by small primes, try potential primes
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{
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size_t i = 211;
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while (true)
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{
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std::size_t q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 10;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 8;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 8;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 6;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 4;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 2;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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i += 10;
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q = n / i;
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if (q < i)
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return n;
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if (n == q * i)
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break;
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// This will loop i to the next "plane" of potential primes
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i += 2;
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}
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}
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next:
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// n is not prime. Increment n to next potential prime.
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if (++in == M)
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{
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++k0;
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in = 0;
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}
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n = L * k0 + indices[in];
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}
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}
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_LIBCPP_END_NAMESPACE_STD
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