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>
const int MAXN = 1e5;
long long ans;
int n, K, edge;
int size[MAXN * 2 + 5], fst[MAXN * 2 + 5];
char str[MAXN + 5];
struct Edge {
  int to, nxt;
  Edge(int _to = 0, int _nxt = 0) : to(_to), nxt(_nxt) {}
} e[MAXN * 2 + 5];
inline void add_edge(int x, int y) {
  e[++edge] = Edge(y, fst[x]);
  fst[x] = edge;
}
inline int read() {
  register int x = 0, v = 1;
  register char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') v = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * v;
}
namespace SAM {
int Last, Size;
int len[MAXN * 5 + 2], link[MAXN * 2 + 5], nxt[26][MAXN * 2 + 5];
void init() {
  for (int i = 1; i <= Size; ++i) {
    for (int j = 0; j < 26; ++j) nxt[j][i] = 0;
    size[i] = fst[i] = 0;
  }
  Last = Size = 1;
  edge = 0;
}
void extend(int x) {
  x -= 'a';
  int cur = ++Size, p;
  size[cur] = 1;
  len[cur] = len[Last] + 1;
  for (p = Last; p && !nxt[x][p]; p = link[p]) nxt[x][p] = cur;
  if (!p)
    link[cur] = 1;
  else {
    int q = nxt[x][p];
    if (len[q] == len[p] + 1)
      link[cur] = q;
    else {
      int cln = ++Size;
      len[cln] = len[p] + 1;
      link[cln] = link[q];
      for (int i = 0; i < 26; ++i) nxt[i][cln] = nxt[i][q];
      for (; p && nxt[x][p] == q; p = link[p]) nxt[x][p] = cln;
      link[cur] = link[q] = cln;
    }
  }
  Last = cur;
}
}  // namespace SAM
using namespace SAM;
void dfs(int x) {
  for (int k = fst[x]; k; k = e[k].nxt) {
    int to = e[k].to;
    dfs(to);
    size[x] += size[to];
  }
  ans += 1LL * (len[x] - len[link[x]]) * size[x] * size[x];
}
int main() {
  int cases = read();
  while (cases--) {
    scanf("%s", str + 1);
    n = strlen(str + 1);
    init();
    for (int i = 1; i <= n; ++i) extend(str[i]);
    for (int i = 2; i <= Size; ++i) add_edge(link[i], i);
    ans = 0;
    dfs(1);
    printf("%lld\n", ans);
  }
  return 0;
}