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;

long long int a[212345], pos[212345], resp;
int n;


int main() {
    scanf("%d", &n);
    for(int i = 1; i <= n; i++) scanf("%lld", &a[i]), pos[a[i]] = i;
    set < int > s;
    s.insert(0);
    s.insert(n+1);
    for(int i = 1; i <= n; i++){
        int l, r;
        s.insert(pos[i]);
        set<int>::iterator it = s.find(pos[i]);
        r = *(++it) - pos[i];
        --it;
        l = pos[i] - *(--it);
        resp += (long)i*r*l;
    }
    printf("%lld\n", resp);
    
    return 0;
}