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>
using namespace std;
int len;
long long ans;
string s;
vector<int> suffix_array, lcp;
int classes = 1;
vector<int> c, cn, p, l, r, cnt;
vector<bool> y;
stack<int> x;
long long f(long long x) { return x * (x + 1) / 2; }
void build() {
  cnt.resize(max(len + 10, 300));
  s.push_back(0);
  len++;
  suffix_array.resize(len);
  cnt['a'] = 1;
  for (int i = 0; i < len; i++) cnt[s[i]]++;
  for (int i = 'b'; i <= 'z'; i++) cnt[i] += cnt[i - 1];
  for (int i = 0; i < len - 1; i++) suffix_array[--cnt[s[i]]] = i;
  suffix_array[0] = len - 1;
  c.resize(len);
  c[len - 1] = 0;
  for (int i = 1; i < len; i++) {
    if (s[suffix_array[i - 1]] < s[suffix_array[i]]) classes++;
    c[suffix_array[i]] = classes - 1;
  }
  cn.resize(len);
  p.resize(len);
  for (int k = 1; k < len; k <<= 1) {
    for (int i = 0; i < classes; i++) cnt[i] = 0;
    for (int i = 0; i < len; i++) {
      p[i] = suffix_array[i] - k;
      if (p[i] < 0) p[i] += len;
    }
    for (int i = 0; i < len; i++) cnt[c[p[i]]]++;
    for (int i = 1; i < classes; i++) cnt[i] += cnt[i - 1];
    for (int i = len - 1; i >= 0; i--) suffix_array[--cnt[c[p[i]]]] = p[i];
    classes = 1;
    cn[0] = 0;
    for (int i = 1; i < len; i++) {
      int a = suffix_array[i - 1] + k, b = suffix_array[i] + k;
      if (a >= len) a -= len;
      if (b >= len) b -= len;
      if (c[suffix_array[i - 1]] != c[suffix_array[i]] || c[a] != c[b])
        classes++;
      cn[suffix_array[i]] = classes - 1;
    }
    for (int i = 0; i < len; i++) c[i] = cn[i];
  }
  lcp.resize(len - 1);
  for (int i = 0; i < len; i++) p[suffix_array[i]] = i;
  int l = 0;
  for (int i = 0; i < len; i++) {
    l = max(l - 1, 0);
    int q = p[i] + 1;
    if (q < len) {
      while (s[i + l] == s[suffix_array[q] + l]) l++;
      lcp[q - 1] = l;
    }
  }
  len--;
  for (int i = 0; i < len; i++) {
    suffix_array[i] = suffix_array[i + 1];
    if (i != len - 1) lcp[i] = lcp[i + 1];
  }
  lcp.pop_back();
  suffix_array.pop_back();
}
int main() {
  cin >> s;
  len = (int)s.length();
  build();
  for (int i = 0; i < len; i++) {
    int l = 0;
    if (i != 0) l = lcp[i - 1];
    if (i != len - 1) l = max(l, lcp[i]);
    ans += len - suffix_array[i] - l;
  }
  l.resize(len);
  r.resize(len);
  x.push(-1);
  y.assign(len, false);
  for (int i = 0; i < len - 1; i++) {
    while (x.top() != -1 && lcp[x.top()] > lcp[i]) x.pop();
    if (x.top() != -1 && lcp[x.top()] == lcp[i]) {
      x.pop();
      y[i] = true;
    }
    l[i] = x.top();
    x.push(i);
  }
  while (!x.empty()) x.pop();
  x.push(len - 1);
  for (int i = len - 2; i >= 0; i--) {
    while (x.top() != len - 1 && lcp[x.top()] >= lcp[i]) x.pop();
    r[i] = x.top();
    x.push(i);
  }
  for (int i = 0; i < len - 1; i++)
    if (!y[i]) {
      int k = 0;
      if (l[i] != -1) k = lcp[l[i]];
      if (r[i] != len - 1) k = max(k, lcp[r[i]]);
      ans += (lcp[i] - k) * f(r[i] - l[i]);
    }
  cout << ans;
  return 0;
}