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;
int min(int a, int b) { return (a < b) ? a : b; }
int max(int a, int b) { return (a > b) ? a : b; }
void bmin(int &a, int b) { a = (a < b) ? a : b; }
void bmax(int &a, int b) { a = (a > b) ? a : b; }
int read() {
  int x = 0, w = 1;
  char ch = getchar();
  while (ch > '9' || ch < '0') {
    if (ch == '-') w = -1;
    ch = getchar();
  }
  while (ch <= '9' && ch >= '0') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * w;
}
const int N = 1e5 + 1, M = 26;
int n, k;
char s[N];
struct Suffix_Automaton {
  int len[N << 1], tr[N << 1][M], fa[N << 1], las = 1, cnt = 1;
  int buc[N], ord[N << 1], siz[N << 1];
  void Init() {
    memset(tr, 0, sizeof(tr));
    memset(len, 0, sizeof(len));
    memset(fa, 0, sizeof(fa));
    memset(siz, 0, sizeof(siz));
    memset(buc, 0, sizeof(buc));
    memset(ord, 0, sizeof(ord));
    las = cnt = 1;
  }
  void Insert(int c) {
    int p = las, q = las = ++cnt;
    len[q] = len[p] + 1;
    siz[q] = 1;
    for (; p && !tr[p][c]; p = fa[p]) tr[p][c] = q;
    if (!p) {
      fa[q] = 1;
      return;
    }
    int np = tr[p][c];
    if (len[np] == len[p] + 1) {
      fa[q] = np;
      return;
    }
    int nq = ++cnt;
    memcpy(tr[nq], tr[np], sizeof(tr[nq]));
    fa[nq] = fa[np];
    fa[np] = fa[q] = nq;
    len[nq] = len[p] + 1;
    for (; p && tr[p][c] == np; p = fa[p]) tr[p][c] = nq;
  }
  long long Query() {
    for (int i = 1; i <= cnt; i++) buc[len[i]]++;
    for (int i = 1; i <= n; i++) buc[i] += buc[i - 1];
    for (int i = 1; i <= cnt; i++) ord[buc[len[i]]--] = i;
    bool fl = 0;
    for (int i = cnt, p = ord[i]; i; i--, p = ord[i]) siz[fa[p]] += siz[p];
    long long ans = 0, res = 0;
    for (int i = 1; i <= cnt; i++) {
      res = 1ll * siz[i] * siz[i];
      ans = ans + res * (len[i] - len[fa[i]]);
    }
    return ans;
  }
} sam;
int main() {
  int T = read();
  while (T--) {
    sam.Init();
    scanf("%s", s + 1);
    n = strlen(s + 1);
    for (int i = 1; i <= n; i++) sam.Insert(s[i] - 'a');
    printf("%lld\n", sam.Query());
  }
  return 0;
}