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;

int main(){
ll N; cin >> N;
vector<pair<ll,ll>> a(N); 
for(ll i = 0; i < N; i++){ cin >> a[i].first; a[i].second = i+1;}

sort(a.begin(),a.end());

set<ll> se;

se.insert(0); se.insert(N+1);

ll ans = 0;

for(ll i = 0; i < N; i++){
 ll r = a[i].second; 
 se.insert(r);
 auto itr = se.lower_bound(r);
 auto itr1 = itr; auto itr2 = itr;
 
 itr1--; itr2++;
 
 ll res = (r-*itr1)*(*itr2-r);
 ans += res*a[i].first;
 
 }
 
 cout << ans << endl;
 
 return 0;
 }

