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()]
min1=min(arr)
count=arr.count(min1)
index1=arr.index(min1)
k=100000000
arr[index1]=k
k+=1
brr=[]

for i in range(index1+1,len(arr),1):
    if arr[i]==min1:
        arr[i]=k
        k+=1
        ans=abs(index1-i)
        brr.append(ans)
        index1=i
print(min(brr))