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
import java.io.IOException;
import java.io.InputStream;
import java.util.*;
import java.math.BigInteger;
 
public class Main implements Runnable {
	
	static int mod = 1000000007;
	
    public static void main(String[] args) {
    	new Thread(null, new Main(), "", 1024 * 1024 * 1024).start();
    }
    
    public void run() {
        FastScanner sc = new FastScanner();
        
        int n = sc.nextInt();
        int[] h = sc.nextIntArray(n);
        
        long e = largestRectangle(h);
        
        System.out.println(e);   
    }
    
	//ヒストグラム内で作れる最大の長方形の面積
	static long largestRectangle(int[] h){
		
		class Rect{
			int leftid;
			int height;
			public Rect(int leftid, int height){
				this.leftid = leftid;
				this.height = height;
			}
		}
		
		int N = h.length;
		long max = 0;
		
		ArrayDeque<Rect> q = new ArrayDeque<>();	//未完成の長方形リスト
		
		for(int i=0;i<N;i++){
			if(q.isEmpty() || q.peekFirst().height < h[i]){
				q.offerFirst(new Rect(i,h[i]));
			}
			else if(q.peekFirst().height > h[i]){
				int leftid = i;
				while(!q.isEmpty() && q.peekFirst().height >= h[i]){
					Rect r = q.pollFirst();
					leftid = r.leftid;
					max = Math.max(max, (long)(i - r.leftid) * (long)r.height);
				}
				q.offerFirst(new Rect(leftid,h[i]));
			}
		}
		
		while(!q.isEmpty()){
			Rect r = q.pollFirst();
			max = Math.max(max, (long)(N - r.leftid) * (long)r.height);
		}
		
		return max;
	}
}



class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}
	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}
	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}
	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
			throw new NumberFormatException();
		return (int) nl;
	}
	public int[] nextIntArray(int n){
		int[] a = new int[n];
		for(int i=0;i<n;i++){
			a[i] = nextInt();
		}
		return a;
	}
	public Integer[] nextIntegerArray(int n){
		Integer[] a = new Integer[n];
		for(int i=0;i<n;i++){
			a[i] = nextInt();
		}
		return a;
	}
	public double nextDouble() {
		return Double.parseDouble(next());
	}
}
