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;

typedef long long ll;
const int MN = 2e5+5;
ll nxt[MN][2], n, i, arr[MN], ord[MN], ans;

int main(){
    for(scanf("%lld",&n),i=1;i<=n;i++){
        scanf("%lld",&arr[i]);
        ord[i] = i;
        nxt[i][0]=i+1;
        nxt[i][1]=i-1;
    }
    sort(ord+1,ord+n+1,[](ll i,ll j){return arr[i]>arr[j];});
    for(i=1;i<=n;i++){
        ll x = ord[i];
        ll l=nxt[x][1], r=nxt[x][0];
        nxt[l][0]=r; nxt[r][1]=l;
        ans += arr[x]*(r-x)*(x-l);
    }
    printf("%lld\n",ans);
    return 0;
}
