Valid Mountain Array

In this problem, you are given an array of integers. Your task is to determine whether the array represents a valid mountain array. A mountain array is defined as an array where:

1. The length of the array is at least 3.
2. There exists an index ( i ) (( 0 < i < n-1 )) such that:
   • The sequence ( arr[0] ) to ( arr[i] ) is strictly increasing (i.e. ( arr[j] < arr[j+1] ) for all ( 0 \le j < i ));
   • The sequence from ( arr[i] ) to ( arr[n-1] ) is strictly decreasing (i.e. ( arr[j] > arr[j+1] ) for all ( i \le j < n-1 )).

Print "True" if the given array is a valid mountain array, otherwise print "False".

Note: The input is read from standard input and the output should be written to standard output.

inputFormat

The first line contains a single integer ( n ) (the number of elements in the array). The second line contains ( n ) space-separated integers representing the elements of the array.

outputFormat

Output a single word: "True" if the array forms a valid mountain, otherwise "False".## sample

4
0 3 2 1

True