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 sys
taille = int(sys.stdin.readline())
tableau = list(map(int, sys.stdin.readline().split()))
mini = min(tableau)
pre = -1
minDist = 10**7
for loop in range(taille):
	if tableau[loop] == mini:
		if pre == -1:
			pre = loop
		else:
			minDist = min(loop-pre, minDist)
			pre = loop
print(minDist)		