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 = 1e5 + 5;
class SuffixAutomata {
 public:
  struct state {
    int len, link;
    unordered_map<int, int> next;
    state() {
      len = link = 0;
      next.clear();
    }
  };
  long long mem[2 * MAXLEN];
  int sz = 1, last = 0;
  vector<state> st;
  vector<int> terminal;
  void Init(int len) {
    st.clear();
    terminal.clear();
    st.resize(2 * len);
    terminal.resize(2 * len);
    sz = 1;
    last = 0;
    st[0].len = 0;
    st[0].link = -1;
    memset(mem, -1, sizeof(mem));
  }
  void extend(char ccc) {
    int c = ccc - 'a';
    int cur = sz++;
    st[cur].len = st[last].len + 1;
    int p = last;
    while (p != -1 && !st[p].next.count(c)) {
      st[p].next[c] = cur;
      p = st[p].link;
    }
    if (p == -1) {
      st[cur].link = 0;
    } else {
      int q = st[p].next[c];
      if (st[p].len + 1 == st[q].len) {
        st[cur].link = q;
      } else {
        int clone = sz++;
        st[clone].len = st[p].len + 1;
        for (auto y : st[q].next) st[clone].next[y.first] = y.second;
        st[clone].link = st[q].link;
        while (p != -1 && st[p].next[c] == q) {
          st[p].next[c] = clone;
          p = st[p].link;
        }
        st[q].link = st[cur].link = clone;
      }
    }
    last = cur;
  }
  void getTerminal() {
    int p = last;
    while (p > 0) terminal[p] = 1, p = st[p].link;
  }
  void build(string s) {
    Init(s.size());
    for (auto x : s) extend(x);
    getTerminal();
  }
  long long dp(int x) {
    long long &ret = mem[x];
    if (ret != -1) return ret;
    ret = terminal[x];
    for (auto y : st[x].next) {
      ret += dp(y.second);
    }
    return ret;
  }
  void solve(string s) {
    build(s);
    long long ans = 0;
    for (int nd = 1; nd < sz; nd++) {
      long long all_string = st[nd].len - st[st[nd].link].len;
      long long frq = dp(nd);
      ans += (frq * frq * all_string);
    }
    printf("%lld\n", ans);
  }
};
char a[100100];
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    SuffixAutomata SA;
    scanf("%s", &a);
    SA.solve(a);
  }
}