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 lInt(d = None): return map(int, input().split(d))

n, *_ = lInt()
a = list(lInt())
mini = min(a)
p = []
ans = 10000000

for i, v in enumerate(a):
  if v == mini:
    p.append(i)
for i, j in enumerate(p):
  if i > 0 and p[i]-p[i-1] < ans:
    ans = p[i]-p[i-1]

print(ans)

