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 math 

R=lambda:map(int,input().split())

n = int(input())

a = list(R())

x = min(a)

indices= [i for i in range(n) if a[i] == x]

l = indices[0]
r = indices[1]
for i in range(2, len(indices)):
    if indices[i] - indices[i-1] < r - l :
        l = indices[i - 1]
        r = indices[i]
print(r - l)
    
