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
n=input()
a=map(int,raw_input().split())
ans=10**9
ansi=0
min=a[0]
for i in range(1,len(a)):
	if min>a[i]:
		min=a[i]
		ansi=i
		ans=10**9
	elif min==a[i]:
		if ans>=i-ansi:
			ans=i-ansi
		ansi=i
print ans