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;
inline int getint() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = (x << 3) + (x << 1) + (ch ^ 48);
    ch = getchar();
  }
  return (f == 1) ? x : -x;
}
const int maxn = 2e5 + 5;
int last = 1, tot = 1, fa[maxn], len[maxn], siz[maxn], sz, T;
int p[maxn];
long long sum = 0;
struct edge {
  int v, nxt;
  edge() {}
  edge(int vv, int nn) { v = vv, nxt = nn; }
} e[maxn << 1];
inline void add(int u, int v) {
  e[++sz] = edge(v, p[u]);
  p[u] = sz;
}
struct SAM {
  int son[maxn][26];
  inline void init() {
    memset(son, 0, sizeof(son));
    memset(fa, 0, sizeof(fa));
    memset(len, 0, sizeof(len));
    memset(siz, 0, sizeof(siz));
    last = tot = 1;
  }
  inline void insert(int c) {
    int np = ++tot, p = last;
    len[np] = len[p] + 1, last = np;
    while (p && !son[p][c]) son[p][c] = np, p = fa[p];
    if (!p)
      fa[np] = 1;
    else {
      int q = son[p][c];
      if (len[q] == len[p] + 1)
        fa[np] = q;
      else {
        int nq = ++tot;
        memcpy(son[nq], son[q], sizeof(son[q]));
        fa[nq] = fa[q];
        fa[q] = fa[np] = nq;
        len[nq] = len[p] + 1;
        while (p && son[p][c] == q) son[p][c] = nq, p = fa[p];
      }
    }
    siz[np]++;
  }
} sam;
inline void dfs(int u) {
  for (int i = p[u]; i != -1; i = e[i].nxt) {
    int v = e[i].v;
    dfs(v);
    siz[u] += siz[v];
  }
  sum += (1LL * siz[u] * siz[u] * (len[u] - len[fa[u]]));
}
char s[maxn];
int main() {
  scanf("%d", &T);
  while (T--) {
    scanf("%s", s + 1);
    sz = sum = 0;
    memset(p, -1, sizeof(p));
    sam.init();
    int len = strlen(s + 1);
    for (int i = 1; i <= len; ++i) sam.insert(s[i] - 'a');
    for (int i = 2; i <= tot; ++i) add(fa[i], i);
    dfs(1);
    printf("%lld\n", sum);
  }
  return 0;
}