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())
arr = [int(i) for i in input().split()]
m = None
pos = None
dist = n+2

for index, elem in enumerate(arr):
    if (m == None):
        m = elem
        pos = index
    elif (elem == m):
        dist = min(dist, index - pos)
        pos = index
    elif (elem < m):
        m = elem
        pos = index
        dist = n+2

print(dist)