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())
x = input().split()
y = []

for i in x:
	y.append(int(i))

num = min(y)

ind = []
for i in range(n):
	if y[i] == num:
		ind.append(i)

gap = 1000000

for i in range(1, len(ind)):
	if ind[i] - ind[i - 1] < gap:
		gap = ind[i] - ind[i - 1]
		
print(gap)