Minimum Index Distance Between Person and Cake

In the array, 0 is an empty spot, 1 is a person, and 2 is a cake. Find the minimum absolute index difference between any person and any cake; return −1 if either kind is missing. This is not about assigning a different cake to each person.

输入格式

The first line contains n, and the second line contains the array. 1≤n≤200000, and elements are only 0, 1, or 2.

输出格式

Output the single integer required by the problem.

样例 1

输入：

5
0 1 0 2 0

输出：

2

样例 2

输入：

3
2 0 1

输出：

2

样例 3

输入：

3
0 0 2

输出：

-1

样例说明

The answers to the three public examples are, in order: 2; 2; -1. The examples were rechecked by independent enumeration, state search, or direct simulation.