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())
input = raw_input()
arr = map(int, input.split(' '))

min_val_index = 0

for i in range(len(arr)):
  if arr[min_val_index] > arr[i]:
    min_val_index = i

min_count = 10e9
count = 1
for i in range(min_val_index + 1, len(arr)):
  if arr[i] == arr[min_val_index]:
    min_count = min(min_count, count)
    count = 1
  else:
    count = count + 1

print min_count