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;
namespace thecold {
const int Max_n = 1e5 + 5;
int t, len[Max_n << 1], link[Max_n << 1], buk[Max_n], ch[Max_n << 1][28];
int siz[Max_n << 1], lst = 1, tot = 1, n, ord[Max_n << 1];
char c[Max_n];
inline int insert(const int x) {
  int newpos = ++tot, p = lst, q, clone;
  len[newpos] = len[lst] + 1, siz[newpos] = 1;
  while (p && !ch[p][x]) ch[p][x] = newpos, p = link[p];
  if (!p) return link[newpos] = 1, newpos;
  q = ch[p][x];
  if (len[q] == len[p] + 1) return link[newpos] = q, newpos;
  clone = ++tot;
  len[clone] = len[p] + 1;
  link[clone] = link[q], link[q] = link[newpos] = clone;
  memcpy(ch[clone], ch[q], sizeof(ch[q]));
  while (p && ch[p][x] == q) ch[p][x] = clone, p = link[p];
  return newpos;
}
inline void main() {
  scanf("%d", &t);
  while (t--) {
    scanf("%s", c + 1);
    n = strlen(c + 1);
    for (int i = 1; i <= n; ++i) lst = insert(c[i] - 'a');
    long long ans = 0;
    for (int i = 1; i <= tot; ++i) ++buk[len[i]];
    for (int i = 1; i <= n; ++i) buk[i] += buk[i - 1];
    for (int i = 1; i <= tot; ++i) ord[buk[len[i]]--] = i;
    for (int i = tot; i; --i) {
      int now = ord[i];
      ans += 1ll * (len[now] - len[link[now]]) * siz[now] * siz[now],
          siz[link[now]] += siz[now];
    }
    printf("%lld\n", ans);
    for (int i = 0; i <= tot; ++i) len[i] = siz[i] = link[i] = ord[i] = 0;
    lst = tot = 1, memset(ch, 0, sizeof(ch));
    for (int i = 1; i <= n; ++i) buk[i] = c[i] = 0;
  }
}
}  // namespace thecold
int main() {
  thecold::main();
  return 0;
}