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;
#define rep(i,n) for(int i=0;i<n;i++)
typedef long long ll;
int main(){
    ll n,A[200000],B[200000]={0},ans=0;
  
    cin>>n;
  
    rep(i,n)
      cin>>A[i],B[A[i]]=i+1;
  
    set<ll> C;
  
    C.insert(0),C.insert(n+1);
  
    rep(i,n) ans+=(i+1)*(B[i+1]-(*--C.lower_bound(B[i+1])))*(*C.upper_bound(B[i+1])-B[i+1]),C.insert(B[i+1]);
    cout<<ans;
}
