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 read() {
  int x = 0, f = 1, c = getchar();
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) {
    x = (x << 1) + (x << 3) + (c ^ 48);
    c = getchar();
  }
  return f == 1 ? x : -x;
}
const int N = 2e5 + 4;
vector<int> e[N];
namespace sam {
struct node {
  int nxt[26], link, len, cl;
} t[N];
int las, siz;
inline void init() {
  for (int i = 0; i < siz; i++) {
    memset(t[i].nxt, 0, sizeof(t[i].nxt));
    t[i].link = t[i].len = t[i].cl = 0;
    e[i].clear();
  }
  siz = 1;
  las = 0;
  t[0].len = 0;
  t[0].link = -1;
}
inline void extend(int c) {
  static int cur, p, q, clo;
  t[cur = siz++].len = t[las].len + 1;
  for (p = las; p != -1 && !t[p].nxt[c]; p = t[p].link) t[p].nxt[c] = cur;
  if (p == -1) {
    t[cur].link = 0;
    las = cur;
    return;
  }
  q = t[p].nxt[c];
  if (t[p].len + 1 == t[q].len) {
    t[cur].link = q;
    las = cur;
    return;
  }
  t[clo = siz++] = t[q];
  t[clo].len = t[p].len + 1;
  t[clo].cl = 1;
  for (; p != -1 && t[p].nxt[c] == q; p = t[p].link) t[p].nxt[c] = clo;
  t[q].link = t[cur].link = clo;
  las = cur;
}
inline void addedge() {
  for (int i = 1; i < siz; i++) e[t[i].link].push_back(i);
}
}  // namespace sam
int n, f[N];
char s[N];
long long ans;
void dfs(int x) {
  if (!sam::t[x].cl)
    f[x] = 1;
  else
    f[x] = 0;
  for (auto v : e[x]) {
    dfs(v);
    f[x] += f[v];
  }
  if (x)
    ans +=
        (long long)f[x] * f[x] * (sam::t[x].len - sam::t[sam::t[x].link].len);
}
int main() {
  for (int T = read(); T--;) {
    scanf("%s", s + 1);
    n = strlen(s + 1);
    sam::init();
    for (int i = 1; i <= n; i++) sam::extend(s[i] - 'a');
    sam::addedge();
    ans = 0;
    dfs(0);
    cout << ans << "\n";
  }
  return (0 - 0);
}