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
def mindist(l):
    f = 'ndone'
    if max(l) == min(l):
        return 1
    smallest = max(l) - min(l)
    for i in range(1, len(l)):
        if l[i] - l[i-1] == 1:
            f = 'done'
            return 1
        elif l[i] - l[i-1] < smallest:
            smallest = l[i] - l[i-1]
    if f == 'ndone':
        return smallest
n = int(input())
a = list(map(int, input().split()))
minimum = min(a)
pos = []
for i in range(len(a)):
    if a[i] == minimum:
        pos.append(i)
print(mindist(pos))

