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

input()
arr = [int(x) for x in input().split()]
minval = min(arr)
minarr, i = [], 0
while True:
	try:
		mi = arr.index(minval, i)
	except ValueError:
		break
	minarr.append(mi)
	i = mi + 1
print(min(abs(x-y) for x, y in zip(minarr, minarr[1:])))
