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
input()

A = list(map(int, input().split()))
x = min(A)

ind = []
for i, a in enumerate(A):
    if a == x:
        ind += [i]
        
ans = ind[1] - ind[0]

for i in range(2, len(ind)):
    ans = min(ans, ind[i] - ind[i-1])
print(ans)    

 