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
import math
if __name__ == "__main__" :
	n = int(input())
	arr = list(map(int,input().split()))
	min_num = min(arr)
	res = list()
	index = 0
	for num in range(n) :
		if arr[num] == min_num :
			res.append(index)

		index += 1	

	res_num = math.inf	
	for num in range(1,len(res)) :
		res_num = min(res_num,res[num]-res[num-1])

	print(res_num)	