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 main()
{
	int N;
	cin >> N;
	vector<int> pos( N + 1 );
	for( int i = 0; i < N; i++ ) {
		int a;
		cin >> a;
		pos[a] = i + 1;
	}

	set<int> st;
	st.insert( 0 );
	st.insert( N + 1 );
	long long ans = 0;
	for( int i = 1; i < N + 1; i++ ) {
		long long ii = pos[i];
		auto pa = st.insert( ii );
		auto it = pa.first;
		long long l = *prev( it );
		long long r = *next( it );
		ans += ( ii - l ) * ( r - ii ) * i;
	}

	cout << ans << endl;
}
