cf424div2 A. Unimodal Array

A. Unimodal Array

#include<iostream> using namespace std;int n,a[100007];int main(){cin>>n;for(int i=1;i<=n;i++)  scanf("%d",a+i);int L=1,R=n;while(L<n&&a[L]<a[L+1])++L;while(R>1&&a[R]<a[R-1])--R; for(int i=L+1;i<=R;++i)   if(a[L]!=a[i])      return puts("No"),0;      return puts("Yes"),0;  }

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Array of integers is unimodal, if:

• it is strictly increasing in the beginning;
• after that it is constant;
• after that it is strictly decreasing.

The first block (increasing) and the last block (decreasing) may be absent. It is allowed that both of this blocks are absent.

For example, the following three arrays are unimodal: [5, 7, 11, 11, 2, 1], [4, 4, 2], [7], but the following three are not unimodal: [5, 5, 6, 6, 1], [1, 2, 1, 2], [4, 5, 5, 6].

Write a program that checks if an array is unimodal.

Input

The first line contains integer n (1 ≤ n ≤ 100) — the number of elements in the array.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 1 000) — the elements of the array.

Output

Print "YES" if the given array is unimodal. Otherwise, print "NO".

You can output each letter in any case (upper or lower).

Examples

input

61 5 5 5 4 2

output

YES

input

510 20 30 20 10

output

YES

input

41 2 1 2

output

NO

input

73 3 3 3 3 3 3

output

YES

Note

In the first example the array is unimodal, because it is strictly increasing in the beginning (from position 1 to position 2, inclusively), that it is constant (from position 2 to position 4, inclusively) and then it is strictly decreasing (from position 4 to position 6, inclusively).