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
def getNext(index):
  for a in range(index+1,len(arr)):
    if arr[a] == minimum:
      return a
  return -1
N = int(input())
arr = list(map(int, input().split()))
minimum = min(arr)
start = arr.index(minimum)
best = float("inf")
nextIndex = getNext(start)
while nextIndex != -1:
  best = min(best,nextIndex-start)
  start,nextIndex = nextIndex,getNext(nextIndex)
print(best)