A histogram is made of a number of contiguous bars, which have same width.

For a given histogram with $N$ bars which have a width of 1 and a height of $h_i$ = $h_1, h_2, ... , h_N$ respectively, find the area of the largest rectangular area.

Constraints

* $1 \leq N \leq 10^5$
* $0 \leq h_i \leq 10^9$

Input

The input is given in the following format.

$N$
$h_1$ $h_2$ ... $h_N$

Output

Print the area of the largest rectangle.

Examples

Input

8
2 1 3 5 3 4 2 1


Output

12


Input

3
2 0 1


Output

2
#include <bits/stdc++.h>
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define srep(i,s,t) for(int i = s; i < t; ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
using namespace std;
typedef long long int ll;
typedef pair<int,int> P;
#define yn {puts("Yes");}else{puts("No");}
#define MAX_N 200005

int n;
int h[MAX_N];

int L[MAX_N], R[MAX_N];
int st[MAX_N];

long long calc(){
    // Lの計算
    int t = 0;
    for(int i = 0; i < n; i++){
        while(t > 0 && h[st[t-1]] >= h[i]) t--;
        L[i] = t == 0 ? 0 : (st[t-1] + 1);
        st[t++] = i;
    }

    // Rの計算
    t = 0;
    for(int i = n - 1; i >= 0; i--){
        while(t > 0 && h[st[t-1]] >= h[i]) t--;
        R[i] = t == 0 ? n : st[t-1];
        st[t++] = i;
    }

    long long res = 0;
    for(int i = 0; i < n; i++){
        res = max(res, (long long)h[i] * (R[i] - L[i]));
    }
    return res;
}

int main() {
    cin >> n;
    rep(i,n)cin >> h[i];
    ll ans = calc();
    cout << ans << endl;
    return 0;
}



