You are given an array of n integer numbers a0, a1, ..., an - 1. Find the distance between two closest (nearest) minimums in it. It is guaranteed that in the array a minimum occurs at least two times.

Input

The first line contains positive integer n (2 ≤ n ≤ 105) — size of the given array. The second line contains n integers a0, a1, ..., an - 1 (1 ≤ ai ≤ 109) — elements of the array. It is guaranteed that in the array a minimum occurs at least two times.

Output

Print the only number — distance between two nearest minimums in the array.

Examples

Input

2
3 3


Output

1


Input

3
5 6 5


Output

2


Input

9
2 1 3 5 4 1 2 3 1


Output

3
def NearestMins():
    n = int(raw_input())
    arr = raw_input().split()
    nums = []
    for i in arr:
        nums.append(int(i))
    minel = min(nums)
    min_indices = []
    for i in range(n):
        if nums[i] == minel:
            min_indices.append(i)
        
    min_diff = float("inf")

    for i in range(len(min_indices)-1):
        diff = min_indices[i+1]-min_indices[i]
        if diff < min_diff:
            min_diff = diff
        
    print min_diff

NearestMins()