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;
const int N = 200010;
int n;
char s[N];
int tot, last;
int ch[N][27], len[N], fa[N];
int size[N];
void Insert(int c) {
  int p = last, np = ++tot;
  len[np] = len[p] + 1;
  for (; !ch[p][c] && p; p = fa[p]) ch[p][c] = np;
  if (!p)
    fa[np] = 1;
  else {
    int q = ch[p][c];
    if (len[q] == len[p] + 1)
      fa[np] = q;
    else {
      int nq = ++tot;
      memcpy(ch[nq], ch[q], sizeof(ch[nq]));
      len[nq] = len[p] + 1;
      fa[nq] = fa[q];
      fa[q] = nq;
      fa[np] = nq;
      for (; ch[p][c] == q; p = fa[p]) ch[p][c] = nq;
    }
  }
  last = np, size[np] = 1;
}
int tong[N], A[N];
void Sort() {
  for (int i = 1; i <= tot; i++) tong[len[i]]++;
  for (int i = 1; i <= n; i++) tong[i] += tong[i - 1];
  for (int i = 1; i <= tot; i++) A[tong[len[i]]--] = i;
}
int mian() {
  memset(fa, 0, sizeof(fa));
  memset(len, 0, sizeof(len));
  memset(size, 0, sizeof(size));
  memset(tong, 0, sizeof(tong));
  memset(ch, 0, sizeof(ch));
  tot = last = 1;
  scanf("%s", &s[1]);
  n = strlen(s + 1);
  for (int i = 1; i <= n; i++) Insert(s[i] - 'a' + 1);
  Sort();
  for (int i = tot; i >= 1; i--) {
    int u = A[i];
    size[fa[u]] += size[u];
  }
  long long Ans = 0;
  for (int i = 1; i <= tot; i++)
    Ans += 1ll * (len[i] - len[fa[i]]) * size[i] * size[i];
  printf("%lld\n", Ans);
  return 0;
}
int main() {
  int T;
  scanf("%d", &T);
  while (T-- > 0) mian();
  return 0;
}