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>
using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
const ull mod = 1e9 + 7;
#define REP(i,n) for(int i=0;i<(int)n;++i)
const int MAX_N = 100005;
int L[MAX_N], R[MAX_N], st[MAX_N];

ll renctangle_in_histgram(vector<ll> &h){
    int N = h.size();
    int t = 0;
    REP(i, N){
        while(t>0 && h[st[t-1]]>=h[i]) t--;
        L[i] = t == 0 ? 0 : (st[t-1]+1);
        st[t++] = i;
    }

    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;
    }

    ll res = 0;
    REP(i, N) res = max(res, (ll)h[i]*(R[i] - L[i]));
    return res;
}

int main(){
    int N;
    cin >> N;
    vector<ll> h(N);
    REP(i, N) cin >> h[i];
    printf("%lld\n", renctangle_in_histgram(h));
    return 0;
}