One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

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Constraints

* 1 ≦ N ≦ 200,000
* (a_1, a_2, ..., a_N) is a permutation of (1, 2, ..., N).

Input

The input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print the answer.

Note that the answer may not fit into a 32-bit integer.

Examples

Input

3
2 1 3


Output

9


Input

4
1 3 2 4


Output

19


Input

8
5 4 8 1 2 6 7 3


Output

85
#include <bits/stdc++.h>
using namespace std;
int n,m,i,j,a,b[200200],l[200200],r[200200];
long long res;
int main() {
  scanf("%d",&n);
  for (i=1; i<=n; i++) {
    scanf("%d",&a);
    b[a]=i;
  }
  for (i=n; i>0; i--) {
    j=b[i];
    l[j]=r[j]=j;
    if (j>1 && r[j-1]!=0) l[j]=l[j-1];
    if (j<n && l[j+1]!=0) r[j]=r[j+1];
    l[r[j]]=l[j];
    r[l[j]]=r[j];
    res+=(j-l[j]+1LL)*(r[j]-j+1LL)*i;
  }
  printf("%lld\n",res);
  return 0;
}
