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 long long ll;
#define REP(i,n) FOR(i,0,n)
#define FOR(i,a,b) for(ll i=a;i<b;i++)
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define PQ priority_queue
#define UM unordered_map
#define ALL(a) (a).begin(),(a).end()
typedef vector<ll> vi;
typedef vector<vector<ll>> vvi;
const ll INF = (1ll << 60);
typedef pair<ll,ll> pii;

ll largestAreaHistogram(vi v){
  ll N=v.size();
  stack<pii> st; st.push({0,v[0]});
  ll ans=v[0];
  FOR(i,1,N) {
    ll tmp=i;
    while(st.size()&&st.top().second>v[i]) {
      ans=max(ans,st.top().second*(i-st.top().first));
      tmp=st.top().first;
      st.pop();
    }
    st.push({tmp,v[i]});
  }
  while(st.size()) {ans=max(ans,st.top().second*(N-st.top().first)); st.pop();}
  return ans;
}

int main(){
  ll N; cin>>N;
  vi h(N); REP(i,N) cin>>h[i];
  cout<<largestAreaHistogram(h)<<endl;
}