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;
class StringDataStructures {
 public:
  int n;
  string s;
  vector<int> sa;
  vector<int> rnk;
  vector<int> lcp;
  vector<int> llcp;
  vector<int> rlcp;
  StringDataStructures(string s) : s(s) {
    n = s.size();
    buildsa();
    buildlcp();
    buildllcp();
    buildrlcp();
  }
  void buildsa() {
    sa.resize(n);
    rnk.resize(n);
    for (int i = 0; i < n; i++) {
      sa[i] = i;
    }
    sort(sa.begin(), sa.end(), [&](int x, int y) { return s[x] < s[y]; });
    vector<int> oldsa(n);
    vector<int> oldrnk(n);
    vector<int> pos(n + 1);
    for (int len = 1;; len *= 2) {
      int cnt = 0;
      swap(rnk, oldrnk);
      for (int i = 0; i < n; i++) {
        int x = sa[i];
        bool eq;
        if (i == 0) {
          eq = false;
        } else {
          int w = sa[i - 1];
          if (len == 1) {
            eq = s[w] == s[x];
          } else {
            eq = oldrnk[w] == oldrnk[x] &&
                 oldrnk[w + len / 2] == oldrnk[x + len / 2];
          }
        }
        if (eq) {
          pos[cnt]++;
        } else {
          pos[++cnt] = 1;
        }
        rnk[x] = cnt - 1;
      }
      if (cnt == n) {
        break;
      }
      pos[0] = 0;
      for (int i = 1; i <= cnt; i++) {
        pos[i] += pos[i - 1];
      }
      swap(sa, oldsa);
      for (int i = n - len; i < n; i++) {
        sa[pos[rnk[i]]++] = i;
      }
      for (int i = 0; i < n; i++) {
        int x = oldsa[i] - len;
        if (x >= 0) {
          sa[pos[rnk[x]]++] = x;
        }
      }
    }
  }
  void buildlcp() {
    lcp.resize(n);
    for (int i = 0, len = 0; i < n - 1; i++) {
      int h = sa[rnk[i] - 1];
      while (s[h + len] == s[i + len]) {
        len++;
      }
      lcp[rnk[i]] = len;
      if (len > 0) {
        len--;
      }
    }
  }
  void buildllcp() {
    llcp.assign(lcp.begin(), lcp.end());
    for (int stp = 2; stp < n; stp *= 2) {
      for (int i = stp; i < n; i += stp) {
        llcp[i] = min(llcp[i], llcp[i - stp / 2]);
      }
    }
  }
  void buildrlcp() {
    rlcp.assign(lcp.begin() + 1, lcp.end());
    rlcp.push_back(0);
    for (int stp = 2; stp < n; stp *= 2) {
      for (int i = 0; i < n; i += stp) {
        rlcp[i] = i + stp >= n ? 0 : min(rlcp[i], rlcp[i + stp / 2]);
      }
    }
  }
  int count(const string& t) {
    int stp = 1;
    while (stp * 2 < n) {
      stp *= 2;
    }
    int lo = 0;
    for (int w = 0, y = 0; stp; stp /= 2) {
      int mi = lo + stp;
      if (mi >= n) {
        y = 0;
        continue;
      }
      int x;
      bool b;
      if (w < y) {
        x = min(y, rlcp[mi]);
        b = y == rlcp[mi];
      } else {
        x = min(w, llcp[mi]);
        b = w == llcp[mi];
      }
      if (b) {
        int m = t.size();
        while (x < m && s[sa[mi] + x] == t[x]) {
          x++;
        }
        if (x == m) {
          int lo = mi, up = mi;
          do {
            if (rlcp[lo - stp] >= m) {
              lo -= stp;
            }
            if (up + stp < n && llcp[up + stp] >= m) {
              up += stp;
            }
            stp /= 2;
          } while (stp);
          return up + 1 - lo;
        }
      }
      if (s[sa[mi] + x] < t[x]) {
        lo = mi;
        w = x;
      } else {
        y = x;
      }
    }
    return 0;
  }
};
int main() {
  ios::sync_with_stdio(false);
  string s;
  cin >> s;
  s += '\0';
  StringDataStructures S(s);
  vector<pair<int, int>> a;
  long long ans = 0;
  for (int i = 0; i < S.n; i++) {
    while (!a.empty() && S.lcp[i] <= a.back().first) {
      a.pop_back();
    }
    a.emplace_back(S.lcp[i], i - 1);
    int z = i == S.n - 1 ? 0 : S.lcp[i + 1];
    for (auto it = a.rbegin(); it != a.rend(); ++it) {
      int w = max(it->first, z);
      int x;
      if (it == a.rbegin()) {
        x = S.n - S.sa[i] - w;
      } else {
        x = (it - 1)->first - w;
      }
      int y = i - it->second;
      ans += (long long)x * y * (y + 1) / 2;
      if (w <= z) {
        break;
      }
    }
  }
  ans -= S.n;
  printf("%lld\n", ans);
  return 0;
}