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, fa[200010], son[200010][26], len[200010], val[200010], cnt, las,
    c[200010], sa[200010];
long long ans;
char s[200010];
void add(int c) {
  int now = ++cnt, p = las;
  len[now] = len[p] + 1;
  while (p && !son[p][c]) son[p][c] = now, p = fa[p];
  if (!p)
    fa[now] = 1;
  else {
    int q = son[p][c];
    if (len[q] == len[p] + 1)
      fa[now] = q;
    else {
      int nq = ++cnt;
      memcpy(son[nq], son[q], sizeof son[q]);
      fa[nq] = fa[q];
      len[nq] = len[p] + 1;
      while (p && son[p][c] == q) son[p][c] = nq, p = fa[p];
      fa[now] = fa[q] = nq;
    }
  }
  ++val[now];
  las = now;
}
int main() {
  scanf("%d", &T);
  while (T--) {
    ans = 0;
    cnt = las = 1;
    memset(son, 0, sizeof(son));
    memset(c, 0, sizeof(c));
    memset(val, 0, sizeof(val));
    scanf("%s", s + 1);
    n = strlen(s + 1);
    for (int i = 1; i <= n; ++i) add(s[i] - 'a');
    for (int i = 1; i <= cnt; ++i) ++c[len[i]];
    for (int i = 1; i <= n; ++i) c[i] += c[i - 1];
    for (int i = cnt; i >= 1; --i) sa[c[len[i]]--] = i;
    for (int i = cnt; i >= 1; --i) {
      int k = sa[i];
      ans += (long long)(len[k] - len[fa[k]]) * val[k] * val[k];
      val[fa[k]] += val[k];
    }
    printf("%lld\n", ans);
  }
}