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
n = int(raw_input())
arr = list(map(int,raw_input().split()))

x = arr[:]
x.sort()

a = x[0]

li = []
dist =  10000000000000
flag = 1
for i in range(n):
    if arr[i] == a and flag :
        flag = 0
        prev = i 
    elif arr[i]==a:
        dist = min(dist,i-prev)
        prev = i
print(dist)




