permutations.java

a molecular graph kernel based on iterative graph similarity and optimal assignments

				--idx; ++j;                                     	// Read into s from the right, into a from the left.
				if (idx == -1) return result;	                  	// Only n(n-1)...(n-k+1) can cause this.
			}
			
			// Find smallest number to increment with.
			while (j > 0 && a[j-1] > result[residx][idx]) --j;
			
			// Rebuild suffix.
			int t = result[residx][idx]; result[residx][idx] = a[j]; a[j] = t;  // Swap symbols from s and a.
			if (idx+1 < k) j = 0; else if (j+1 < n-k) ++j;
			while (idx+1 < k) {
				++idx;
				result[residx][idx] = a[0];
				for (int i = 0; i < alength-1; ++i) { a[i] = a[i+1]; } --alength;  // Remove first symbol from a.
			}
			if (residx+1 < result.length) { System.arraycopy(result[residx], 0, result[residx+1], 0, k); ++residx; }
		}
	}
	
	// Precomputed prefixes.
	
	static final int[][][][] prefixPrecomp = {
		{ {} },  // n = 0.
		{ {}, {{0}} },  // n = 1.
		{ {}, {{0},{1}}, {{0,1},{1,0}} },  // n = 2.
		{ {}, {{0},{1},{2}}, {{0,1},{0,2},{1,0},{1,2},{2,0},{2,1}}, {{0,1,2},{0,2,1},{1,0,2},{1,2,0},{2,0,1},{2,1,0}} },  // n = 3.
		{ {}, {{0},{1},{2},{3}}, {{0,1},{0,2},{0,3},{1,0},{1,2},{1,3},{2,0},{2,1},{2,3},{3,0},{3,1},{3,2}},  // n = 4.
			{{0,1,2},{0,1,3},{0,2,1},{0,2,3},{0,3,1},{0,3,2},{1,0,2},{1,0,3},{1,2,0},{1,2,3},{1,3,0},{1,3,2},
			{2,0,1},{2,0,3},{2,1,0},{2,1,3},{2,3,0},{2,3,1},{3,0,1},{3,0,2},{3,1,0},{3,1,2},{3,2,0},{3,2,1}},
			{{0,1,2,3},{0,1,3,2},{0,2,1,3},{0,2,3,1},{0,3,1,2},{0,3,2,1},{1,0,2,3},{1,0,3,2},{1,2,0,3},{1,2,3,0},{1,3,0,2},{1,3,2,0},
			{2,0,1,3},{2,0,3,1},{2,1,0,3},{2,1,3,0},{2,3,0,1},{2,3,1,0},{3,0,1,2},{3,0,2,1},{3,1,0,2},{3,1,2,0},{3,2,0,1},{3,2,1,0}} },
		{ {}, {{0},{1},{2},{3},{4}}, {{0,1},{0,2},{0,3},{0,4},{1,0},{1,2},{1,3},{1,4},{2,0},{2,1},{2,3},{2,4},{3,0},{3,1},{3,2},{3,4},{4,0},{4,1},{4,2},{4,3}},  // n = 5.
			{{0,1,2},{0,1,3},{0,1,4},{0,2,1},{0,2,3},{0,2,4},{0,3,1},{0,3,2},{0,3,4},{0,4,1},{0,4,2},{0,4,3},{1,0,2},{1,0,3},{1,0,4},{1,2,0},{1,2,3},{1,2,4},
			{1,3,0},{1,3,2},{1,3,4},{1,4,0},{1,4,2},{1,4,3},{2,0,1},{2,0,3},{2,0,4},{2,1,0},{2,1,3},{2,1,4},{2,3,0},{2,3,1},{2,3,4},{2,4,0},{2,4,1},{2,4,3},
			{3,0,1},{3,0,2},{3,0,4},{3,1,0},{3,1,2},{3,1,4},{3,2,0},{3,2,1},{3,2,4},{3,4,0},{3,4,1},{3,4,2},{4,0,1},{4,0,2},{4,0,3},{4,1,0},{4,1,2},{4,1,3},
			{4,2,0},{4,2,1},{4,2,3},{4,3,0},{4,3,1},{4,3,2}},
			{ {0,1,2,3},{0,1,2,4},{0,1,3,2},{0,1,3,4},{0,1,4,2},{0,1,4,3},{0,2,1,3},{0,2,1,4},{0,2,3,1},{0,2,3,4},{0,2,4,1},{0,2,4,3},{0,3,1,2},{0,3,1,4},{0,3,2,1},
			{0,3,2,4},{0,3,4,1},{0,3,4,2},{0,4,1,2},{0,4,1,3},{0,4,2,1},{0,4,2,3},{0,4,3,1},{0,4,3,2},{1,0,2,3},{1,0,2,4},{1,0,3,2},{1,0,3,4},{1,0,4,2},{1,0,4,3},
			{1,2,0,3},{1,2,0,4},{1,2,3,0},{1,2,3,4},{1,2,4,0},{1,2,4,3},{1,3,0,2},{1,3,0,4},{1,3,2,0},{1,3,2,4},{1,3,4,0},{1,3,4,2},{1,4,0,2},{1,4,0,3},{1,4,2,0},
			{1,4,2,3},{1,4,3,0},{1,4,3,2},{2,0,1,3},{2,0,1,4},{2,0,3,1},{2,0,3,4},{2,0,4,1},{2,0,4,3},{2,1,0,3},{2,1,0,4},{2,1,3,0},{2,1,3,4},{2,1,4,0},{2,1,4,3},
			{2,3,0,1},{2,3,0,4},{2,3,1,0},{2,3,1,4},{2,3,4,0},{2,3,4,1},{2,4,0,1},{2,4,0,3},{2,4,1,0},{2,4,1,3},{2,4,3,0},{2,4,3,1},{3,0,1,2},{3,0,1,4},{3,0,2,1},
			{3,0,2,4},{3,0,4,1},{3,0,4,2},{3,1,0,2},{3,1,0,4},{3,1,2,0},{3,1,2,4},{3,1,4,0},{3,1,4,2},{3,2,0,1},{3,2,0,4},{3,2,1,0},{3,2,1,4},{3,2,4,0},{3,2,4,1},
			{3,4,0,1},{3,4,0,2},{3,4,1,0},{3,4,1,2},{3,4,2,0},{3,4,2,1},{4,0,1,2},{4,0,1,3},{4,0,2,1},{4,0,2,3},{4,0,3,1},{4,0,3,2},{4,1,0,2},{4,1,0,3},{4,1,2,0},
			{4,1,2,3},{4,1,3,0},{4,1,3,2},{4,2,0,1},{4,2,0,3},{4,2,1,0},{4,2,1,3},{4,2,3,0},{4,2,3,1},{4,3,0,1},{4,3,0,2},{4,3,1,0},{4,3,1,2},{4,3,2,0},{4,3,2,1} },
            { {0,1,2,3,4},{0,1,2,4,3},{0,1,3,2,4},{0,1,3,4,2},{0,1,4,2,3},{0,1,4,3,2},{0,2,1,3,4},{0,2,1,4,3},{0,2,3,1,4},{0,2,3,4,1},{0,2,4,1,3},{0,2,4,3,1},
			{0,3,1,2,4},{0,3,1,4,2},{0,3,2,1,4},{0,3,2,4,1},{0,3,4,1,2},{0,3,4,2,1},{0,4,1,2,3},{0,4,1,3,2},{0,4,2,1,3},{0,4,2,3,1},{0,4,3,1,2},{0,4,3,2,1},{1,0,2,3,4},
			{1,0,2,4,3},{1,0,3,2,4},{1,0,3,4,2},{1,0,4,2,3},{1,0,4,3,2},{1,2,0,3,4},{1,2,0,4,3},{1,2,3,0,4},{1,2,3,4,0},{1,2,4,0,3},{1,2,4,3,0},{1,3,0,2,4},{1,3,0,4,2},
			{1,3,2,0,4},{1,3,2,4,0},{1,3,4,0,2},{1,3,4,2,0},{1,4,0,2,3},{1,4,0,3,2},{1,4,2,0,3},{1,4,2,3,0},{1,4,3,0,2},{1,4,3,2,0},{2,0,1,3,4},{2,0,1,4,3},{2,0,3,1,4},
			{2,0,3,4,1},{2,0,4,1,3},{2,0,4,3,1},{2,1,0,3,4},{2,1,0,4,3},{2,1,3,0,4},{2,1,3,4,0},{2,1,4,0,3},{2,1,4,3,0},{2,3,0,1,4},{2,3,0,4,1},{2,3,1,0,4},{2,3,1,4,0},
			{2,3,4,0,1},{2,3,4,1,0},{2,4,0,1,3},{2,4,0,3,1},{2,4,1,0,3},{2,4,1,3,0},{2,4,3,0,1},{2,4,3,1,0},{3,0,1,2,4},{3,0,1,4,2},{3,0,2,1,4},{3,0,2,4,1},{3,0,4,1,2},
			{3,0,4,2,1},{3,1,0,2,4},{3,1,0,4,2},{3,1,2,0,4},{3,1,2,4,0},{3,1,4,0,2},{3,1,4,2,0},{3,2,0,1,4},{3,2,0,4,1},{3,2,1,0,4},{3,2,1,4,0},{3,2,4,0,1},{3,2,4,1,0},
			{3,4,0,1,2},{3,4,0,2,1},{3,4,1,0,2},{3,4,1,2,0},{3,4,2,0,1},{3,4,2,1,0},{4,0,1,2,3},{4,0,1,3,2},{4,0,2,1,3},{4,0,2,3,1},{4,0,3,1,2},{4,0,3,2,1},{4,1,0,2,3},
			{4,1,0,3,2},{4,1,2,0,3},{4,1,2,3,0},{4,1,3,0,2},{4,1,3,2,0},{4,2,0,1,3},{4,2,0,3,1},{4,2,1,0,3},{4,2,1,3,0},{4,2,3,0,1},{4,2,3,1,0},{4,3,0,1,2},{4,3,0,2,1},
			{4,3,1,0,2},{4,3,1,2,0},{4,3,2,0,1},{4,3,2,1,0} } },
        { {}, { {0},{1},{2},{3},{4},{5} },  // n = 6
          { {0,1},{0,2},{0,3},{0,4},{0,5}, {1,0},{1,2},{1,3},{1,4},{1,5}, {2,0},{2,1},{2,3},{2,4},{2,5},
            {3,0},{3,1},{3,2},{3,4},{3,5}, {4,0},{4,1},{4,2},{4,3},{4,5}, {5,0},{5,1},{5,2},{5,3},{5,4} },
          { {0,1,2},{0,1,3},{0,1,4},{0,1,5},{0,2,1},{0,2,3},{0,2,4},{0,2,5},{0,3,1},{0,3,2},{0,3,4},{0,3,5},{0,4,1},{0,4,2},{0,4,3},{0,4,5},{0,5,1},{0,5,2},{0,5,3},{0,5,4},
            {1,0,2},{1,0,3},{1,0,4},{1,0,5},{1,2,0},{1,2,3},{1,2,4},{1,2,5},{1,3,0},{1,3,2},{1,3,4},{1,3,5},{1,4,0},{1,4,2},{1,4,3},{1,4,5},{1,5,0},{1,5,2},{1,5,3},{1,5,4},
            {2,0,1},{2,0,3},{2,0,4},{2,0,5},{2,1,0},{2,1,3},{2,1,4},{2,1,5},{2,3,0},{2,3,1},{2,3,4},{2,3,5},{2,4,0},{2,4,1},{2,4,3},{2,4,5},{2,5,0},{2,5,1},{2,5,3},{2,5,4},
            {3,0,1},{3,0,2},{3,0,4},{3,0,5},{3,1,0},{3,1,2},{3,1,4},{3,1,5},{3,2,0},{3,2,1},{3,2,4},{3,2,5},{3,4,0},{3,4,1},{3,4,2},{3,4,5},{3,5,0},{3,5,1},{3,5,2},{3,5,4},
            {4,0,1},{4,0,2},{4,0,3},{4,0,5},{4,1,0},{4,1,2},{4,1,3},{4,1,5},{4,2,0},{4,2,1},{4,2,3},{4,2,5},{4,3,0},{4,3,1},{4,3,2},{4,3,5},{4,5,0},{4,5,1},{4,5,2},{4,5,3},
            {5,0,1},{5,0,2},{5,0,3},{5,0,4},{5,1,0},{5,1,2},{5,1,3},{5,1,4},{5,2,0},{5,2,1},{5,2,3},{5,2,4},{5,3,0},{5,3,1},{5,3,2},{5,3,4},{5,4,0},{5,4,1},{5,4,2},{5,4,3} },
          { {0,1,2,3},{0,1,2,4},{0,1,2,5},{0,1,3,2},{0,1,3,4},{0,1,3,5},{0,1,4,2},{0,1,4,3},{0,1,4,5},{0,1,5,2},{0,1,5,3},{0,1,5,4},
            {0,2,1,3},{0,2,1,4},{0,2,1,5},{0,2,3,1},{0,2,3,4},{0,2,3,5},{0,2,4,1},{0,2,4,3},{0,2,4,5},{0,2,5,1},{0,2,5,3},{0,2,5,4},
            {0,3,1,2},{0,3,1,4},{0,3,1,5},{0,3,2,1},{0,3,2,4},{0,3,2,5},{0,3,4,1},{0,3,4,2},{0,3,4,5},{0,3,5,1},{0,3,5,2},{0,3,5,4},
            {0,4,1,2},{0,4,1,3},{0,4,1,5},{0,4,2,1},{0,4,2,3},{0,4,2,5},{0,4,3,1},{0,4,3,2},{0,4,3,5},{0,4,5,1},{0,4,5,2},{0,4,5,3},
            {0,5,1,2},{0,5,1,3},{0,5,1,4},{0,5,2,1},{0,5,2,3},{0,5,2,4},{0,5,3,1},{0,5,3,2},{0,5,3,4},{0,5,4,1},{0,5,4,2},{0,5,4,3},
            {1,0,2,3},{1,0,2,4},{1,0,2,5},{1,0,3,2},{1,0,3,4},{1,0,3,5},{1,0,4,2},{1,0,4,3},{1,0,4,5},{1,0,5,2},{1,0,5,3},{1,0,5,4},
            {1,2,0,3},{1,2,0,4},{1,2,0,5},{1,2,3,0},{1,2,3,4},{1,2,3,5},{1,2,4,0},{1,2,4,3},{1,2,4,5},{1,2,5,0},{1,2,5,3},{1,2,5,4},
            {1,3,0,2},{1,3,0,4},{1,3,0,5},{1,3,2,0},{1,3,2,4},{1,3,2,5},{1,3,4,0},{1,3,4,2},{1,3,4,5},{1,3,5,0},{1,3,5,2},{1,3,5,4},
            {1,4,0,2},{1,4,0,3},{1,4,0,5},{1,4,2,0},{1,4,2,3},{1,4,2,5},{1,4,3,0},{1,4,3,2},{1,4,3,5},{1,4,5,0},{1,4,5,2},{1,4,5,3},
            {1,5,0,2},{1,5,0,3},{1,5,0,4},{1,5,2,0},{1,5,2,3},{1,5,2,4},{1,5,3,0},{1,5,3,2},{1,5,3,4},{1,5,4,0},{1,5,4,2},{1,5,4,3},
            {2,0,1,3},{2,0,1,4},{2,0,1,5},{2,0,3,1},{2,0,3,4},{2,0,3,5},{2,0,4,1},{2,0,4,3},{2,0,4,5},{2,0,5,1},{2,0,5,3},{2,0,5,4},
            {2,1,0,3},{2,1,0,4},{2,1,0,5},{2,1,3,0},{2,1,3,4},{2,1,3,5},{2,1,4,0},{2,1,4,3},{2,1,4,5},{2,1,5,0},{2,1,5,3},{2,1,5,4},
            {2,3,0,1},{2,3,0,4},{2,3,0,5},{2,3,1,0},{2,3,1,4},{2,3,1,5},{2,3,4,0},{2,3,4,1},{2,3,4,5},{2,3,5,0},{2,3,5,1},{2,3,5,4},
            {2,4,0,1},{2,4,0,3},{2,4,0,5},{2,4,1,0},{2,4,1,3},{2,4,1,5},{2,4,3,0},{2,4,3,1},{2,4,3,5},{2,4,5,0},{2,4,5,1},{2,4,5,3},
            {2,5,0,1},{2,5,0,3},{2,5,0,4},{2,5,1,0},{2,5,1,3},{2,5,1,4},{2,5,3,0},{2,5,3,1},{2,5,3,4},{2,5,4,0},{2,5,4,1},{2,5,4,3},
            {3,0,1,2},{3,0,1,4},{3,0,1,5},{3,0,2,1},{3,0,2,4},{3,0,2,5},{3,0,4,1},{3,0,4,2},{3,0,4,5},{3,0,5,1},{3,0,5,2},{3,0,5,4},
            {3,1,0,2},{3,1,0,4},{3,1,0,5},{3,1,2,0},{3,1,2,4},{3,1,2,5},{3,1,4,0},{3,1,4,2},{3,1,4,5},{3,1,5,0},{3,1,5,2},{3,1,5,4},
            {3,2,0,1},{3,2,0,4},{3,2,0,5},{3,2,1,0},{3,2,1,4},{3,2,1,5},{3,2,4,0},{3,2,4,1},{3,2,4,5},{3,2,5,0},{3,2,5,1},{3,2,5,4},
            {3,4,0,1},{3,4,0,2},{3,4,0,5},{3,4,1,0},{3,4,1,2},{3,4,1,5},{3,4,2,0},{3,4,2,1},{3,4,2,5},{3,4,5,0},{3,4,5,1},{3,4,5,2},
            {3,5,0,1},{3,5,0,2},{3,5,0,4},{3,5,1,0},{3,5,1,2},{3,5,1,4},{3,5,2,0},{3,5,2,1},{3,5,2,4},{3,5,4,0},{3,5,4,1},{3,5,4,2},
            {4,0,1,2},{4,0,1,3},{4,0,1,5},{4,0,2,1},{4,0,2,3},{4,0,2,5},{4,0,3,1},{4,0,3,2},{4,0,3,5},{4,0,5,1},{4,0,5,2},{4,0,5,3},
            {4,1,0,2},{4,1,0,3},{4,1,0,5},{4,1,2,0},{4,1,2,3},{4,1,2,5},{4,1,3,0},{4,1,3,2},{4,1,3,5},{4,1,5,0},{4,1,5,2},{4,1,5,3},
            {4,2,0,1},{4,2,0,3},{4,2,0,5},{4,2,1,0},{4,2,1,3},{4,2,1,5},{4,2,3,0},{4,2,3,1},{4,2,3,5},{4,2,5,0},{4,2,5,1},{4,2,5,3},
            {4,3,0,1},{4,3,0,2},{4,3,0,5},{4,3,1,0},{4,3,1,2},{4,3,1,5},{4,3,2,0},{4,3,2,1},{4,3,2,5},{4,3,5,0},{4,3,5,1},{4,3,5,2},
            {4,5,0,1},{4,5,0,2},{4,5,0,3},{4,5,1,0},{4,5,1,2},{4,5,1,3},{4,5,2,0},{4,5,2,1},{4,5,2,3},{4,5,3,0},{4,5,3,1},{4,5,3,2},
            {5,0,1,2},{5,0,1,3},{5,0,1,4},{5,0,2,1},{5,0,2,3},{5,0,2,4},{5,0,3,1},{5,0,3,2},{5,0,3,4},{5,0,4,1},{5,0,4,2},{5,0,4,3},
            {5,1,0,2},{5,1,0,3},{5,1,0,4},{5,1,2,0},{5,1,2,3},{5,1,2,4},{5,1,3,0},{5,1,3,2},{5,1,3,4},{5,1,4,0},{5,1,4,2},{5,1,4,3},
            {5,2,0,1},{5,2,0,3},{5,2,0,4},{5,2,1,0},{5,2,1,3},{5,2,1,4},{5,2,3,0},{5,2,3,1},{5,2,3,4},{5,2,4,0},{5,2,4,1},{5,2,4,3},
            {5,3,0,1},{5,3,0,2},{5,3,0,4},{5,3,1,0},{5,3,1,2},{5,3,1,4},{5,3,2,0},{5,3,2,1},{5,3,2,4},{5,3,4,0},{5,3,4,1},{5,3,4,2},
            {5,4,0,1},{5,4,0,2},{5,4,0,3},{5,4,1,0},{5,4,1,2},{5,4,1,3},{5,4,2,0},{5,4,2,1},{5,4,2,3},{5,4,3,0},{5,4,3,1},{5,4,3,2} },             
          { {0,1,2,3,4},{0,1,2,3,5},{0,1,2,4,3},{0,1,2,4,5},{0,1,2,5,3},{0,1,2,5,4},{0,1,3,2,4},{0,1,3,2,5},{0,1,3,4,2},{0,1,3,4,5},{0,1,3,5,2},{0,1,3,5,4},
            {0,1,4,2,3},{0,1,4,2,5},{0,1,4,3,2},{0,1,4,3,5},{0,1,4,5,2},{0,1,4,5,3},{0,1,5,2,3},{0,1,5,2,4},{0,1,5,3,2},{0,1,5,3,4},{0,1,5,4,2},{0,1,5,4,3},
            {0,2,1,3,4},{0,2,1,3,5},{0,2,1,4,3},{0,2,1,4,5},{0,2,1,5,3},{0,2,1,5,4},{0,2,3,1,4},{0,2,3,1,5},{0,2,3,4,1},{0,2,3,4,5},{0,2,3,5,1},{0,2,3,5,4},
            {0,2,4,1,3},{0,2,4,1,5},{0,2,4,3,1},{0,2,4,3,5},{0,2,4,5,1},{0,2,4,5,3},{0,2,5,1,3},{0,2,5,1,4},{0,2,5,3,1},{0,2,5,3,4},{0,2,5,4,1},{0,2,5,4,3},
            {0,3,1,2,4},{0,3,1,2,5},{0,3,1,4,2},{0,3,1,4,5},{0,3,1,5,2},{0,3,1,5,4},{0,3,2,1,4},{0,3,2,1,5},{0,3,2,4,1},{0,3,2,4,5},{0,3,2,5,1},{0,3,2,5,4},
            {0,3,4,1,2},{0,3,4,1,5},{0,3,4,2,1},{0,3,4,2,5},{0,3,4,5,1},{0,3,4,5,2},{0,3,5,1,2},{0,3,5,1,4},{0,3,5,2,1},{0,3,5,2,4},{0,3,5,4,1},{0,3,5,4,2},
            {0,4,1,2,3},{0,4,1,2,5},{0,4,1,3,2},{0,4,1,3,5},{0,4,1,5,2},{0,4,1,5,3},{0,4,2,1,3},{0,4,2,1,5},{0,4,2,3,1},{0,4,2,3,5},{0,4,2,5,1},{0,4,2,5,3},
            {0,4,3,1,2},{0,4,3,1,5},{0,4,3,2,1},{0,4,3,2,5},{0,4,3,5,1},{0,4,3,5,2},{0,4,5,1,2},{0,4,5,1,3},{0,4,5,2,1},{0,4,5,2,3},{0,4,5,3,1},{0,4,5,3,2},
            {0,5,1,2,3},{0,5,1,2,4},{0,5,1,3,2},{0,5,1,3,4},{0,5,1,4,2},{0,5,1,4,3},{0,5,2,1,3},{0,5,2,1,4},{0,5,2,3,1},{0,5,2,3,4},{0,5,2,4,1},{0,5,2,4,3},
            {0,5,3,1,2},{0,5,3,1,4},{0,5,3,2,1},{0,5,3,2,4},{0,5,3,4,1},{0,5,3,4,2},{0,5,4,1,2},{0,5,4,1,3},{0,5,4,2,1},{0,5,4,2,3},{0,5,4,3,1},{0,5,4,3,2},
            {1,0,2,3,4},{1,0,2,3,5},{1,0,2,4,3},{1,0,2,4,5},{1,0,2,5,3},{1,0,2,5,4},{1,0,3,2,4},{1,0,3,2,5},{1,0,3,4,2},{1,0,3,4,5},{1,0,3,5,2},{1,0,3,5,4},
            {1,0,4,2,3},{1,0,4,2,5},{1,0,4,3,2},{1,0,4,3,5},{1,0,4,5,2},{1,0,4,5,3},{1,0,5,2,3},{1,0,5,2,4},{1,0,5,3,2},{1,0,5,3,4},{1,0,5,4,2},{1,0,5,4,3},
            {1,2,0,3,4},{1,2,0,3,5},{1,2,0,4,3},{1,2,0,4,5},{1,2,0,5,3},{1,2,0,5,4},{1,2,3,0,4},{1,2,3,0,5},{1,2,3,4,0},{1,2,3,4,5},{1,2,3,5,0},{1,2,3,5,4},
            {1,2,4,0,3},{1,2,4,0,5},{1,2,4,3,0},{1,2,4,3,5},{1,2,4,5,0},{1,2,4,5,3},{1,2,5,0,3},{1,2,5,0,4},{1,2,5,3,0},{1,2,5,3,4},{1,2,5,4,0},{1,2,5,4,3},
            {1,3,0,2,4},{1,3,0,2,5},{1,3,0,4,2},{1,3,0,4,5},{1,3,0,5,2},{1,3,0,5,4},{1,3,2,0,4},{1,3,2,0,5},{1,3,2,4,0},{1,3,2,4,5},{1,3,2,5,0},{1,3,2,5,4},
            {1,3,4,0,2},{1,3,4,0,5},{1,3,4,2,0},{1,3,4,2,5},{1,3,4,5,0},{1,3,4,5,2},{1,3,5,0,2},{1,3,5,0,4},{1,3,5,2,0},{1,3,5,2,4},{1,3,5,4,0},{1,3,5,4,2},
            {1,4,0,2,3},{1,4,0,2,5},{1,4,0,3,2},{1,4,0,3,5},{1,4,0,5,2},{1,4,0,5,3},{1,4,2,0,3},{1,4,2,0,5},{1,4,2,3,0},{1,4,2,3,5},{1,4,2,5,0},{1,4,2,5,3},
            {1,4,3,0,2},{1,4,3,0,5},{1,4,3,2,0},{1,4,3,2,5},{1,4,3,5,0},{1,4,3,5,2},{1,4,5,0,2},{1,4,5,0,3},{1,4,5,2,0},{1,4,5,2,3},{1,4,5,3,0},{1,4,5,3,2},
            {1,5,0,2,3},{1,5,0,2,4},{1,5,0,3,2},{1,5,0,3,4},{1,5,0,4,2},{1,5,0,4,3},{1,5,2,0,3},{1,5,2,0,4},{1,5,2,3,0},{1,5,2,3,4},{1,5,2,4,0},{1,5,2,4,3},
            {1,5,3,0,2},{1,5,3,0,4},{1,5,3,2,0},{1,5,3,2,4},{1,5,3,4,0},{1,5,3,4,2},{1,5,4,0,2},{1,5,4,0,3},{1,5,4,2,0},{1,5,4,2,3},{1,5,4,3,0},{1,5,4,3,2},
            {2,0,1,3,4},{2,0,1,3,5},{2,0,1,4,3},{2,0,1,4,5},{2,0,1,5,3},{2,0,1,5,4},{2,0,3,1,4},{2,0,3,1,5},{2,0,3,4,1},{2,0,3,4,5},{2,0,3,5,1},{2,0,3,5,4},
            {2,0,4,1,3},{2,0,4,1,5},{2,0,4,3,1},{2,0,4,3,5},{2,0,4,5,1},{2,0,4,5,3},{2,0,5,1,3},{2,0,5,1,4},{2,0,5,3,1},{2,0,5,3,4},{2,0,5,4,1},{2,0,5,4,3},
            {2,1,0,3,4},{2,1,0,3,5},{2,1,0,4,3},{2,1,0,4,5},{2,1,0,5,3},{2,1,0,5,4},{2,1,3,0,4},{2,1,3,0,5},{2,1,3,4,0},{2,1,3,4,5},{2,1,3,5,0},{2,1,3,5,4},
            {2,1,4,0,3},{2,1,4,0,5},{2,1,4,3,0},{2,1,4,3,5},{2,1,4,5,0},{2,1,4,5,3},{2,1,5,0,3},{2,1,5,0,4},{2,1,5,3,0},{2,1,5,3,4},{2,1,5,4,0},{2,1,5,4,3},
            {2,3,0,1,4},{2,3,0,1,5},{2,3,0,4,1},{2,3,0,4,5},{2,3,0,5,1},{2,3,0,5,4},{2,3,1,0,4},{2,3,1,0,5},{2,3,1,4,0},{2,3,1,4,5},{2,3,1,5,0},{2,3,1,5,4},
            {2,3,4,0,1},{2,3,4,0,5},{2,3,4,1,0},{2,3,4,1,5},{2,3,4,5,0},{2,3,4,5,1},{2,3,5,0,1},{2,3,5,0,4},{2,3,5,1,0},{2,3,5,1,4},{2,3,5,4,0},{2,3,5,4,1},
            {2,4,0,1,3},{2,4,0,1,5},{2,4,0,3,1},{2,4,0,3,5},{2,4,0,5,1},{2,4,0,5,3},{2,4,1,0,3},{2,4,1,0,5},{2,4,1,3,0},{2,4,1,3,5},{2,4,1,5,0},{2,4,1,5,3},
            {2,4,3,0,1},{2,4,3,0,5},{2,4,3,1,0},{2,4,3,1,5},{2,4,3,5,0},{2,4,3,5,1},{2,4,5,0,1},{2,4,5,0,3},{2,4,5,1,0},{2,4,5,1,3},{2,4,5,3,0},{2,4,5,3,1},
            {2,5,0,1,3},{2,5,0,1,4},{2,5,0,3,1},{2,5,0,3,4},{2,5,0,4,1},{2,5,0,4,3},{2,5,1,0,3},{2,5,1,0,4},{2,5,1,3,0},{2,5,1,3,4},{2,5,1,4,0},{2,5,1,4,3},
            {2,5,3,0,1},{2,5,3,0,4},{2,5,3,1,0},{2,5,3,1,4},{2,5,3,4,0},{2,5,3,4,1},{2,5,4,0,1},{2,5,4,0,3},{2,5,4,1,0},{2,5,4,1,3},{2,5,4,3,0},{2,5,4,3,1},
            {3,0,1,2,4},{3,0,1,2,5},{3,0,1,4,2},{3,0,1,4,5},{3,0,1,5,2},{3,0,1,5,4},{3,0,2,1,4},{3,0,2,1,5},{3,0,2,4,1},{3,0,2,4,5},{3,0,2,5,1},{3,0,2,5,4},
            {3,0,4,1,2},{3,0,4,1,5},{3,0,4,2,1},{3,0,4,2,5},{3,0,4,5,1},{3,0,4,5,2},{3,0,5,1,2},{3,0,5,1,4},{3,0,5,2,1},{3,0,5,2,4},{3,0,5,4,1},{3,0,5,4,2},
            {3,1,0,2,4},{3,1,0,2,5},{3,1,0,4,2},{3,1,0,4,5},{3,1,0,5,2},{3,1,0,5,4},{3,1,2,0,4},{3,1,2,0,5},{3,1,2,4,0},{3,1,2,4,5},{3,1,2,5,0},{3,1,2,5,4},