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
var row = readline().split(" ").map(function(x) { return parseInt(x); });
var n = row[0];

var a = [];
row = readline().split(" ").map(function(x) { return parseInt(x); });
for(var i = 0; i < n; i++) {
	a.push(row[i]);
}

var result = 0;
var min = a[0];
var resultMin = -1;
for(var i = 1; i < n; i++) {
	if(a[i] < min) {
		min = a[i];
		result = 0;
                resultMin = -1;
	} else if (a[i] > min) {
		result++;
	} else {
		if(resultMin == -1) {
			resultMin = result + 1;
		} else {
			if(resultMin > result + 1) {
				resultMin = result + 1;
			}
		}
		result = 0;
	}
}

write(resultMin);