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 NMAX = 100000 + 5;
struct State {
  int len, link;
  int cnt, dp;
  bool vis;
  int trans[26];
} states[2 * NMAX];
int sz, last;
void init() {
  sz = last = 0;
  memset(states, 0, sizeof states);
  states[0].link = -1;
}
void addLetter(int letter) {
  int current = ++sz;
  states[current].len = states[last].len + 1;
  int p;
  for (p = last; p != -1 && !states[p].trans[letter]; p = states[p].link)
    states[p].trans[letter] = current;
  if (p != -1) {
    int q = states[p].trans[letter];
    if (states[p].len + 1 == states[q].len)
      states[current].link = q;
    else {
      int clone = ++sz;
      states[clone] = states[q];
      states[clone].len = states[p].len + 1;
      for (; p != -1 && states[p].trans[letter] == q; p = states[p].link)
        states[p].trans[letter] = clone;
      states[q].link = states[current].link = clone;
    }
  }
  last = current;
}
void dfs(int node) {
  if (states[node].vis) return;
  states[node].vis = true;
  for (int i = 0; i < 26; ++i)
    if (states[node].trans[i]) {
      dfs(states[node].trans[i]);
      states[node].dp += states[states[node].trans[i]].dp;
    }
}
int main() {
  ios_base ::sync_with_stdio(false);
  cin.tie(0);
  int T = 0;
  cin >> T;
  while (T--) {
    string str;
    cin >> str;
    init();
    for (auto it : str) addLetter(it - 'a');
    for (int i = 1; i <= sz; ++i) {
      assert(states[i].link != -1);
      states[i].cnt = states[i].len - states[states[i].link].len;
    }
    int node = last;
    while (node) {
      states[node].dp = 1;
      node = states[node].link;
    }
    dfs(0);
    long long int ans = 0;
    for (int i = 1; i <= sz; ++i) {
      ans += 1LL * states[i].cnt * states[i].dp * states[i].dp;
    }
    cout << ans << '\n';
  }
  return 0;
}