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 MAXLEN = 100005;
struct state {
  int len, link, siz;
  map<char, int> nxt;
  friend bool operator<(state &x, state &y) { return x.len < y.len; }
} st[MAXLEN * 2];
int sz, last;
void SAM_Init() {
  st[0].len = 0;
  st[0].link = -1;
  st[0].nxt.clear();
  sz = 0;
  last = 0;
}
void SAM_Extend(char c) {
  int cur = ++sz;
  st[cur].len = st[last].len + 1;
  st[cur].nxt.clear();
  int p = last;
  while (p != -1 && !st[p].nxt.count(c)) {
    st[p].nxt[c] = cur;
    p = st[p].link;
  }
  if (p == -1)
    st[cur].link = 0;
  else {
    int q = st[p].nxt[c];
    if (st[p].len + 1 == st[q].len)
      st[cur].link = q;
    else {
      int clone = ++sz;
      st[clone].len = st[p].len + 1;
      st[clone].link = st[q].link;
      st[clone].nxt = st[q].nxt;
      st[clone].siz = 0;
      while (p != -1 && st[p].nxt[c] == q) {
        st[p].nxt[c] = clone;
        p = st[p].link;
      }
      st[q].link = st[cur].link = clone;
    }
  }
  st[cur].siz = 1;
  last = cur;
}
char s[MAXLEN];
int a[2 * MAXLEN];
int cn[2 * MAXLEN], T;
int main() {
  scanf("%d", &T);
  while (T--) {
    scanf("%s", s);
    SAM_Init();
    for (int i = 0; s[i]; i++) SAM_Extend(s[i]);
    for (int i = 0; i <= sz; i++) cn[i] = 0;
    for (int i = 1; i <= sz; i++) cn[st[i].len]++;
    for (int i = 1; i <= sz; i++) cn[i] += cn[i - 1];
    for (int i = sz; i >= 1; i--) a[cn[st[i].len]--] = i;
    long long ans = 0;
    for (int i = sz; i > 0; i--) {
      int d = a[i];
      ans =
          ans + 1ll * (st[d].len - st[st[d].link].len) * st[d].siz * st[d].siz;
      st[st[d].link].siz += st[d].siz;
    }
    printf("%lld\n", ans);
  }
  return 0;
}