Problem: Now that you have proposed a fake post for the HC2 Facebook page, Heidi wants to measure the quality of the post before actually posting it. She recently came across a (possibly fake) article about the impact of fractal structure on multimedia messages and she is now trying to measure the self-similarity of the message, which is defined as

<image>

where the sum is over all nonempty strings p and <image> is the number of occurences of p in s as a substring. (Note that the sum is infinite, but it only has a finite number of nonzero summands.)

Heidi refuses to do anything else until she knows how to calculate this self-similarity. Could you please help her? (If you would like to instead convince Heidi that a finite string cannot be a fractal anyway – do not bother, we have already tried.)

Input

The input starts with a line indicating the number of test cases T (1 ≤ T ≤ 10). After that, T test cases follow, each of which consists of one line containing a string s (1 ≤ |s| ≤ 100 000) composed of lowercase letters (a-z).

Output

Output T lines, every line containing one number – the answer to the corresponding test case.

Example

Input

4
aa
abcd
ccc
abcc


Output

5
10
14
12

Note

A string s contains another string p as a substring if p is a contiguous subsequence of s. For example, ab is a substring of cab but not of acb.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int t, n, ch[200007][30], f[200007], len[200007], sz[200007], id[200007], cnt,
    lst;
char s[100007];
int insert(int c) {
  int p = lst, np = lst = ++cnt;
  len[np] = len[p] + 1;
  while (p && !ch[p][c]) ch[p][c] = np, p = f[p];
  if (!p)
    f[np] = 1;
  else {
    int q = ch[p][c];
    if (len[q] == len[p] + 1)
      f[np] = q;
    else {
      int nq = ++cnt;
      len[nq] = len[p] + 1;
      memcpy(ch[nq], ch[q], sizeof ch[nq]);
      f[nq] = f[q];
      f[q] = f[np] = nq;
      while (ch[p][c] == q) ch[p][c] = nq, p = f[p];
    }
  }
  sz[np] = 1;
  return 0;
}
int cmp(int a, int b) { return len[a] < len[b]; }
int main() {
  scanf("%d", &t);
  for (int lp = 1; lp <= t; lp++) {
    scanf("%s", s + 1);
    n = strlen(s + 1);
    memset(ch, 0, sizeof ch);
    memset(f, 0, sizeof f);
    memset(len, 0, sizeof len);
    memset(sz, 0, sizeof sz);
    cnt = lst = 1;
    for (int i = 1; i <= n; i++) insert(s[i] - 'a');
    for (int i = 1; i <= cnt; i++) id[i] = i;
    sort(id + 1, id + cnt + 1, cmp);
    long long res = 0;
    for (int i = cnt; i >= 1; i--) {
      res += 1LL * (len[id[i]] - len[f[id[i]]]) * sz[id[i]] * sz[id[i]];
      sz[f[id[i]]] += sz[id[i]];
    }
    printf("%lld\n", res);
  }
  return 0;
}