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(raw_input())
inds = [x for x in range(N)]
nums = list(map(int,raw_input().split()))
nums,inds = zip(*sorted(zip(nums,inds)))
cur = nums[0]
ind = 1
ans = 99999999999
while nums[ind] == cur:
  if abs(inds[ind]-inds[ind-1]) < ans:
    ans = abs(inds[ind]-inds[ind-1])
  ind += 1
  if ind == N:
    break
print ans