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 maxn = 2e5 + 10;
const int INF = 0x3f3f3f3f;
int link[maxn], nxt[maxn][26], len[maxn], cnt[maxn], o, last;
void insert(int c) {
  int p = last;
  int cur = ++o;
  len[cur] = len[p] + 1;
  cnt[cur] = 1;
  while (p != -1 && !nxt[p][c]) {
    nxt[p][c] = cur;
    p = link[p];
  }
  if (p == -1)
    link[cur] = 0;
  else {
    int q = nxt[p][c];
    if (len[q] == len[p] + 1)
      link[cur] = q;
    else {
      int clone = ++o;
      memcpy(nxt[clone], nxt[q], sizeof nxt[q]);
      link[clone] = link[q];
      len[clone] = len[p] + 1;
      link[q] = link[cur] = clone;
      while (p != -1 && nxt[p][c] == q) {
        nxt[p][c] = clone;
        p = link[p];
      }
    }
  }
  last = cur;
}
char s[maxn];
int rk[maxn], sa[maxn], tax[maxn];
void Sort() {
  memset(tax, 0, sizeof tax);
  for (int i = 1; i <= o; i++) tax[len[i]]++;
  for (int i = 1; i < maxn; i++) tax[i] += tax[i - 1];
  for (int i = 1; i <= o; i++) sa[i] = tax[len[i]]--;
  for (int i = 1; i <= o; i++) rk[sa[i]] = i;
}
int main(void) {
  int t;
  scanf("%d", &t);
  o = 0;
  while (t--) {
    long long ans = 0;
    scanf("%s", s);
    for (int i = 0; i <= o; i++) {
      memset(nxt[i], 0, sizeof nxt[i]);
      link[i] = 0;
      cnt[i] = len[i] = 0;
    }
    last = o = 0;
    link[0] = -1;
    for (int i = 0; s[i]; i++) insert(s[i] - 'a');
    Sort();
    for (int i = o; i > 0; i--) {
      int x = rk[i];
      int l = 1, r = len[x];
      l = len[link[x]] + 1;
      cnt[link[x]] += cnt[x];
      ans += 1ll * (r - l + 1) * cnt[x] * cnt[x];
    }
    printf("%lld\n", ans);
  }
}