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
import os

import sys

debug = True

if debug and os.path.exists("input.in"):
    input = open("input.in", "r").readline
else:
    debug = False
    input = sys.stdin.readline


def inp():
    return (int(input()))


def inlt():
    return (list(map(int, input().split())))


def insr():
    s = input()
    return s[:len(s) - 1]  # Remove line char from end


def invr():
    return (map(int, input().split()))


test_count = 1
if debug:
    test_count = inp()
for t in range(test_count):
    if debug:
        print("Test Case #", t + 1)
    # Start code here
    n = inp()
    a = inlt()
    m = min(a)
    last = -1
    ans = n
    for i in range(n):
        if a[i] == m:
            if last != -1:
                ans = min(ans, i - last)
            last = i

    print(ans)
