// lexicographic order for pairs
inline bool leq(int a1, int a2, int b1, int b2) {
    return(a1 < b1 || a1 == b1 && a2 <= b2);
}

// and triples
inline bool leq(int a1, int a2, int a3, int b1, int b2, int b3) {
    return(a1 < b1 || a1 == b1 && leq(a2,a3, b2,b3));
} // and triples

// stably sort a[0..n-1] to b[0..n-1] with keys in 0..K from r
static void radixPass(int* a, int* b, int* r, int n, int K) {// count occurrences
    int* c = new int[K + 1]; // counter array
    for (int i = 0; i <= K; i++) c[i] = 0; // reset counters
    for (int i = 0; i < n; i++) c[r[a[i]]]++; // count occurrences
    for (int i = 0, sum = 0; i <= K; i++) // exclusive prefix sums
    {
        int t = c[i];
        c[i] = sum;
        sum += t;
    }
    for (int i = 0;  i < n; i++) b[c[r[a[i]]]++] = a[i]; // sort
    delete [] c;
}

// find the suffix array SA of s[0..n-1] in {1..K}ˆn
// require s[n]=s[n+1]=s[n+2]=0, n>=2
void suffixArray(int* s, int* SA, int n, int K) {
    int n0 = (n+2)/3, n1 = (n+1)/3, n2 = n/3, n02 = n0+n2;
    int* s12 = new int[n02+3]; s12[n02] = s12[n02+1] = s12[n02+2] = 0;
    int* SA12 = new int[n02+3]; SA12[n02] = SA12[n02+1] = SA12[n02+2] = 0;
    int* s0 = new int[n0];
    int* SA0 = new int[n0];
    // generate positions of mod 1 and mod 2 suffixes
    // the "+(n0-n1)" adds a dummy mod 1 suffix if n%3 == 1
    for (int i=0, j=0; i < n + (n0-n1); i++)
        if (i%3 != 0) s12[j++] = i;
    // lsb radix sort the mod 1 and mod 2 triples
    radixPass(s12 , SA12, s+2, n02, K);
    radixPass(SA12, s12 , s+1, n02, K);
    radixPass(s12 , SA12, s  , n02, K);
    // find lexicographic names of triples
    int name = 0, c0 = -1, c1 = -1, c2 = -1;
    for (int i = 0; i < n02; i++) {
        if (s[SA12[i]] != c0 || s[SA12[i]+1] != c1 || s[SA12[i]+2] != c2) {
            name++;
            c0 = s[SA12[i]];
            c1 = s[SA12[i]+1];
            c2 = s[SA12[i]+2];
        }
        if (SA12[i]%3 == 1) s12[SA12[i]/3] = name; // left half
        else s12[SA12[i]/3 + n0] = name; // right half
    }
    // recurse if names are not yet unique
    if (name < n02) {
        suffixArray(s12, SA12, n02, name);
        // store unique names in s12 using the suffix array
        for (int i = 0; i < n02; i++) s12[SA12[i]] = i + 1;
    } else // generate the suffix array of s12 directly
        for (int i = 0;  i < n02; i++) SA12[s12[i] - 1] = i;
    // stably sort the mod 0 suffixes from SA12 by their first character
    for (int i = 0, j = 0; i < n02; i++)
        if (SA12[i] < n0) s0[j++] = 3*SA12[i];
    radixPass(s0, SA0, s, n0, K);
    // merge sorted SA0 suffixes and sorted SA12 suffixes
    for (int p = 0, t = n0-n1, k = 0; k < n; k++) {
        #define GetI() (SA12[t] < n0 ? SA12[t] * 3 + 1 : (SA12[t] - n0) * 3 + 2)
        int i = GetI(); // pos of current offset 12 suffix
        int j = SA0[p]; // pos of current offset 0 suffix
        if (SA12[t] < n0 ? // different compares for mod 1 and mod 2 suffixes
            leq(s[i], s12[SA12[t] + n0], s[j], s12[j/3]) :
            leq(s[i],s[i+1],s12[SA12[t]-n0+1], s[j],s[j+1],s12[j/3+n0]))
        {// suffix from SA12 is smaller
            SA[k] = i; t++;
            if (t == n02) // done --- only SA0 suffixes left
            for (k++; p < n0; p++, k++) SA[k] = SA0[p];
        } else {// suffix from SA0 is smaller
            SA[k] = j; p++;
            if (p == n0) // done --- only SA12 suffixes left
            for (k++; t < n02; t++, k++) SA[k] = GetI();
        }
    }
    delete [] s12; delete [] SA12; delete [] SA0; delete [] s0;
}

int main() {

    return 0;
}