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>
long long ans;
int n, t, k;
char s[200005];
struct SAM {
  int ch[200005][26], step[200005], pre[200005], cnt, last, a[200005],
      b[200005], sz[200005], c[200005];
  inline void init() {
    memset(ch, 0, sizeof ch);
    memset(c, 0, sizeof c);
    memset(a, 0, sizeof a);
    memset(b, 0, sizeof b);
    memset(sz, 0, sizeof sz);
    memset(step, 0, sizeof step);
    memset(pre, 0, sizeof pre);
    cnt = last = 1;
  }
  inline void ins(int x) {
    int p = last, np = ++cnt;
    last = cnt;
    step[np] = step[p] + 1;
    sz[np] = 1;
    while (p && !ch[p][x]) ch[p][x] = np, p = pre[p];
    if (!p)
      pre[np] = 1;
    else {
      int q = ch[p][x];
      if (step[q] == step[p] + 1)
        pre[np] = q;
      else {
        int nq = ++cnt;
        step[nq] = step[p] + 1;
        memcpy(ch[nq], ch[q], sizeof ch[q]);
        pre[nq] = pre[q];
        pre[q] = pre[np] = nq;
        while (ch[p][x] == q) ch[p][x] = nq, p = pre[p];
      }
    }
  }
  inline void solve() {
    int up = 0;
    for (int i = (1); i <= (cnt); ++i) up = std::max(up, step[i]);
    for (int i = (1); i <= (cnt); ++i) a[step[i]]++;
    for (int i = (1); i <= (up); ++i) a[i] += a[i - 1];
    for (int i = (1); i <= (cnt); ++i) b[a[step[i]]--] = i;
    for (int j = (cnt); j >= (1); --j) {
      int i = b[j];
      sz[pre[i]] += sz[i];
    }
    ans = 0;
    for (int i = (2); i <= (cnt); ++i)
      ans += 1ll * sz[i] * sz[i] * (step[i] - step[pre[i]]);
    printf("%lld\n", ans);
  }
} sam;
int main() {
  scanf("%d", &t);
  while (t--) {
    scanf("%s", s + 1);
    n = strlen(s + 1);
    sam.init();
    for (int i = (1); i <= (n); ++i) sam.ins(s[i] - 'a');
    sam.solve();
  }
  return 0;
}