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(x) for x in input().split()]
ar = sorted(arr)
m1 = ar[0]
m2 = ar[1]
arr1 = [int(1e10)]*n
ind = -1
for i in range(n):
    if arr[i] == m2 and ind!=-1:
        arr1[i] = i-ind
    if arr[i] == m1 :
        ind = i
ind = -1
for i in range(n-1,-1,-1):
    if arr[i] == m2 and ind!=-1:
        arr1[i] = min(ind - i,arr1[i])
    if arr[i] == m1 :
        ind = i

arr1 = sorted(arr1)
print(arr1[0])