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>
#include <iostream>
#include <algorithm>
#include <set>
using namespace std;
int main(){
	int N; 
	cin >> N; 
	int A[200010] = {}; 
	int B[200010] = {}; 
	for(int i = 1; i <= N; i++){
		cin >> A[i]; 
		B[A[i]] = i; 
	}
	set<int> used {0, N + 1}; 
	long long int ans = 0; 
	for(int i = 1; i <= N; i++){
		auto it = used.lower_bound(B[i]); 
		long long int R = *it - B[i]; 
		it --; 
		long long int L = B[i] - *it; 
		used.insert(B[i]); 
		ans += (long long) i * R * L; 
	}
	cout << ans << endl; 
}