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>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;

int n, a[200000], b[200001];
int main() {
	scanf("%d", &n);
	rep(i, n) {
		scanf("%d", &a[i]);
		b[a[i]] = i;
	}
	set<int>v;
	ll sum = 0;
	for (ll i = 1; i <= n; i++) {
		auto it = v.lower_bound(b[i]);
		int l, r;
		if (it == v.end())r = n;
		else r = *it;
		if (it == v.begin())l = -1;
		else l = *--it;
		sum += i*(r - b[i])*(b[i] - l);
		v.insert(b[i]);
	}
	printf("%lld\n", sum);
}