Problem: You are given a string s. Each pair of numbers l and r that fulfill the condition 1 ≤ l ≤ r ≤ |s|, correspond to a substring of the string s, starting in the position l and ending in the position r (inclusive).

Let's define the function of two strings F(x, y) like this. We'll find a list of such pairs of numbers for which the corresponding substrings of string x are equal to string y. Let's sort this list of pairs according to the pair's first number's increasing. The value of function F(x, y) equals the number of non-empty continuous sequences in the list.

For example: F(babbabbababbab, babb) = 6. The list of pairs is as follows:

(1, 4), (4, 7), (9, 12)

Its continuous sequences are: 

  * (1, 4)
  * (4, 7)
  * (9, 12)
  * (1, 4), (4, 7)
  * (4, 7), (9, 12)
  * (1, 4), (4, 7), (9, 12)



Your task is to calculate for the given string s the sum F(s, x) for all x, that x belongs to the set of all substrings of a string s.

Input

The only line contains the given string s, consisting only of small Latin letters (1 ≤ |s| ≤ 105).

Output

Print the single number — the sought sum.

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.

Examples

Input

aaaa


Output

20


Input

abcdef


Output

21


Input

abacabadabacaba


Output

188

Note

In the first sample the function values at x equal to "a", "aa", "aaa" and "aaaa" equal 10, 6, 3 and 1 correspondingly.

In the second sample for any satisfying x the function value is 1.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
const int MAXN = 1e5 + 10;
int sa[MAXN], lcp[MAXN];
int rank[MAXN], px[MAXN], temp[MAXN], id[MAXN], cnt[MAXN];
bool cmp(int i, int j, int w) {
  return temp[i] == temp[j] && temp[i + w] == temp[j + w];
}
void calcu_sa(const char *str, int n, int *sa) {
  int p, m = 300;
  memset(cnt, 0, sizeof(cnt));
  for (int i = 0; i <= n; ++i) ++cnt[rank[i] = str[i]];
  for (int i = 1; i <= m; ++i) cnt[i] += cnt[i - 1];
  for (int i = n; i >= 0; --i) sa[--cnt[rank[i]]] = i;
  for (int w = 1; w < n; w <<= 1, m = p) {
    p = 0;
    for (int i = n; i > n - w; --i) id[p++] = i;
    for (int i = 0; i <= n; ++i)
      if (sa[i] >= w) id[p++] = sa[i] - w;
    memset(cnt, 0, sizeof(cnt));
    for (int i = 0; i <= n; ++i) ++cnt[px[i] = rank[id[i]]];
    for (int i = 1; i <= m; ++i) cnt[i] += cnt[i - 1];
    for (int i = n; i >= 0; --i) sa[--cnt[px[i]]] = id[i];
    memcpy(temp, rank, sizeof(rank));
    rank[sa[0]] = (p = 0);
    for (int i = 1; i <= n; ++i)
      rank[sa[i]] = cmp(sa[i], sa[i - 1], w) ? p : ++p;
  }
}
void calcu_lcp(const char *str, int n, int *sa, int *lcp) {
  for (int i = 0; i <= n; ++i) rank[sa[i]] = i;
  for (int i = 0, h = 0; i < n; ++i) {
    int j = sa[rank[i] - 1];
    if (h) --h;
    for (; i + h <= n && j + h <= n; ++h)
      if (str[i + h] != str[j + h]) break;
    lcp[rank[i] - 1] = h;
  }
}
char S[MAXN];
std::pair<int, int> stk[MAXN];
int top;
int main() {
  while (~scanf("%s", S)) {
    int n = strlen(S);
    calcu_sa(S, n, sa);
    calcu_lcp(S, n, sa, lcp);
    long long ans = 1ll * (n + 1) * n / 2;
    long long cnt = 0;
    for (int i = 0; i <= n; ++i) {
      std::pair<int, int> cur(lcp[i], 1);
      while (top && stk[top - 1].first >= cur.first) {
        --top;
        cnt -= 1ll * stk[top].first * stk[top].second;
        cur.second += stk[top].second;
      }
      cnt += cur.first * cur.second;
      stk[top++] = cur;
      ans += cnt;
    }
    printf("%lld\n", ans);
  }
  return 0;
}