Given a non-empty array of non-negative integers, the degree of this array is defined as the maximum frequency of any one of its elements.

Your task is to find the smallest possible length of a (contiguous) subarray of the given array, that has the same degree as the given array.

Input:

1st line contains 'n' the length of the array

2nd line contains n space-separated integers

Example Input

5

1 2 2 3 1

Output: Length of the smallest subarray

Example

Input: 

5

1 2 2 3 1

Output: 2

Explanation: 
The input array has a degree of 2 because both elements 1 and 2 appear twice.
Of the subarrays that have the same degree:
[1, 2, 2, 3, 1], [1, 2, 2, 3], [2, 2, 3, 1], [1, 2, 2], [2, 2, 3], [2, 2]
The shortest length is 2. So answer is 2.

Input:

7

1 2 2 3 1 4 2
Output: 6
Explanation:
The degree is 3 because the element 2 is repeated 3 times.
So [2,2,3,1,4,2] is the shortest subarray, therefore answer is 6.