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;
template <size_t N, size_t M>
struct Suffix_Automata {
  int maxlen[N], trans[N][M], link[N], Size, Last, siz[N];
  Suffix_Automata() { Size = Last = 1; }
  void Extend(int id) {
    int cur = (++Size), p;
    maxlen[cur] = maxlen[Last] + 1;
    siz[cur] = 1;
    for (p = Last; p && !trans[p][id]; p = link[p]) trans[p][id] = cur;
    if (!p)
      link[cur] = 1;
    else {
      int q = trans[p][id];
      if (maxlen[q] == maxlen[p] + 1)
        link[cur] = q;
      else {
        int clone = (++Size);
        maxlen[clone] = maxlen[p] + 1;
        memcpy(trans[clone], trans[q], sizeof(trans[q]));
        link[clone] = link[q];
        for (; p && trans[p][id] == q; p = link[p]) trans[p][id] = clone;
        link[cur] = link[q] = clone;
      }
    }
    Last = cur;
  }
  vector<int> G[N];
  void Build() {
    for (int i = 1; i <= Size; i++) G[i].clear();
    for (int i = 2; i <= Size; i++) G[link[i]].push_back(i);
  }
  void dfs(int u) {
    for (auto v : G[u]) {
      dfs(v);
      siz[u] += siz[v];
    }
  }
};
Suffix_Automata<300000, 26> SAM;
char s[300000];
int main() {
  int T;
  scanf("%d", &T);
  for (int _ = 0; _ < T; _++) {
    memset(SAM.trans, 0, sizeof(SAM.trans));
    memset(SAM.link, 0, sizeof(SAM.link));
    memset(SAM.maxlen, 0, sizeof(SAM.maxlen));
    memset(SAM.siz, 0, sizeof(SAM.siz));
    SAM.Last = SAM.Size = 1;
    scanf("%s", s + 1);
    int n = strlen(s + 1);
    for (int i = 1; i <= n; i++) {
      SAM.Extend(s[i] - 'a');
    }
    SAM.Build();
    SAM.dfs(1);
    long long ans = 0;
    for (int i = 2; i <= SAM.Size; i++) {
      ans += 1LL * SAM.siz[i] * SAM.siz[i] *
             (SAM.maxlen[i] - SAM.maxlen[SAM.link[i]]);
    }
    printf("%lld\n", ans);
  }
  return 0;
}