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 = int(input())
tab = list(map(int, input().split()))
i = tab.index(min(tab))
val = tab[i]
qtab = [i]
for j in range(i+1, n):
	if tab[j] == val:
		qtab.append(j)
if len(qtab) == 1:
	tabx = list(tab)
	tabx.pop(i)
	val = min(tabx)
	j = tab.index(val)
	qt = [j]
	mn = abs(j - qtab[0])
	for u in range(n):
		if tab[u] == val:
			mn = min(mn, abs(u - qtab[0]))
	print(mn)	
else:
	mn = qtab[1] - qtab[0]
	for i in range(2, len(qtab)):
		mn = min(mn, qtab[i] - qtab[i-1])
	print(mn)	