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// lexicographic order for pairs
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inline bool leq(int a1, int a2, int b1, int b2) {
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    return(a1 < b1 || a1 == b1 && a2 <= b2);
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}
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// and triples
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inline bool leq(int a1, int a2, int a3, int b1, int b2, int b3) {
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    return(a1 < b1 || a1 == b1 && leq(a2,a3, b2,b3));
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} // and triples
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// stably sort a[0..n-1] to b[0..n-1] with keys in 0..K from r
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static void radixPass(int* a, int* b, int* r, int n, int K) {// count occurrences
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    int* c = new int[K + 1]; // counter array
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    for (int i = 0; i <= K; i++) c[i] = 0; // reset counters
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    for (int i = 0; i < n; i++) c[r[a[i]]]++; // count occurrences
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    for (int i = 0, sum = 0; i <= K; i++) // exclusive prefix sums
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    {
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        int t = c[i];
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        c[i] = sum;
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        sum += t;
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    }
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    for (int i = 0;  i < n; i++) b[c[r[a[i]]]++] = a[i]; // sort
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    delete [] c;
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}
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// find the suffix array SA of s[0..n-1] in {1..K}ˆn
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// require s[n]=s[n+1]=s[n+2]=0, n>=2
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void suffixArray(int* s, int* SA, int n, int K) {
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    int n0 = (n+2)/3, n1 = (n+1)/3, n2 = n/3, n02 = n0+n2;
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    int* s12 = new int[n02+3]; s12[n02] = s12[n02+1] = s12[n02+2] = 0;
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    int* SA12 = new int[n02+3]; SA12[n02] = SA12[n02+1] = SA12[n02+2] = 0;
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    int* s0 = new int[n0];
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    int* SA0 = new int[n0];
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    // generate positions of mod 1 and mod 2 suffixes
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    // the "+(n0-n1)" adds a dummy mod 1 suffix if n%3 == 1
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    for (int i=0, j=0; i < n + (n0-n1); i++)
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        if (i%3 != 0) s12[j++] = i;
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    // lsb radix sort the mod 1 and mod 2 triples
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    radixPass(s12 , SA12, s+2, n02, K);
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    radixPass(SA12, s12 , s+1, n02, K);
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    radixPass(s12 , SA12, s  , n02, K);
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    // find lexicographic names of triples
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    int name = 0, c0 = -1, c1 = -1, c2 = -1;
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    for (int i = 0; i < n02; i++) {
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        if (s[SA12[i]] != c0 || s[SA12[i]+1] != c1 || s[SA12[i]+2] != c2) {
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            name++;
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            c0 = s[SA12[i]];
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            c1 = s[SA12[i]+1];
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            c2 = s[SA12[i]+2];
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        }
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        if (SA12[i]%3 == 1) s12[SA12[i]/3] = name; // left half
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        else s12[SA12[i]/3 + n0] = name; // right half
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    }
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    // recurse if names are not yet unique
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    if (name < n02) {
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        suffixArray(s12, SA12, n02, name);
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        // store unique names in s12 using the suffix array
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        for (int i = 0; i < n02; i++) s12[SA12[i]] = i + 1;
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    } else // generate the suffix array of s12 directly
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        for (int i = 0;  i < n02; i++) SA12[s12[i] - 1] = i;
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    // stably sort the mod 0 suffixes from SA12 by their first character
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    for (int i = 0, j = 0; i < n02; i++)
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        if (SA12[i] < n0) s0[j++] = 3*SA12[i];
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    radixPass(s0, SA0, s, n0, K);
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    // merge sorted SA0 suffixes and sorted SA12 suffixes
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    for (int p = 0, t = n0-n1, k = 0; k < n; k++) {
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        #define GetI() (SA12[t] < n0 ? SA12[t] * 3 + 1 : (SA12[t] - n0) * 3 + 2)
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        int i = GetI(); // pos of current offset 12 suffix
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        int j = SA0[p]; // pos of current offset 0 suffix
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        if (SA12[t] < n0 ? // different compares for mod 1 and mod 2 suffixes
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            leq(s[i], s12[SA12[t] + n0], s[j], s12[j/3]) :
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            leq(s[i],s[i+1],s12[SA12[t]-n0+1], s[j],s[j+1],s12[j/3+n0]))
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        {// suffix from SA12 is smaller
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            SA[k] = i; t++;
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            if (t == n02) // done --- only SA0 suffixes left
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            for (k++; p < n0; p++, k++) SA[k] = SA0[p];
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        } else {// suffix from SA0 is smaller
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            SA[k] = j; p++;
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            if (p == n0) // done --- only SA12 suffixes left
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            for (k++; t < n02; t++, k++) SA[k] = GetI();
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        }
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    }
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    delete [] s12; delete [] SA12; delete [] SA0; delete [] s0;
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}
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int main() {
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    return 0;
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}