There are $n$ boxes arranged in a row. Among them, two adjacent boxes are empty. The remaining boxes contain $n/2 - 1$ red balls and $n/2 - 1$ green balls. Each box contains at most one ball.

Bajtazar has invented a very interesting game, which consists of moving balls between boxes so that, in the end, all red balls are located before all green balls. In each single move, you are allowed to move two adjacent balls into the empty boxes, provided that their relative order is not changed during this operation. Bajtazar has come to you for help in writing a program to play this game.

The first line of the result file should contain the number of moves $m$ required to perform the sorting. Each of the following $m$ lines should contain a single number $p_k$ ($0 \le p_k \le n - 2$), describing the $k$-th move. The move described by the number $p_k$ consists of moving the ball from box $p_k$ to the left empty box, and the ball from box $p_k + 1$ to the right empty box.

Input

The first line contains a single even integer $n$ ($8 \le n \le 200\,000$), representing the number of boxes on the table. The boxes are numbered from 0, starting from the left. The next line contains an $n$-character string consisting of the digits 0, 1, and 2. The consecutive digits in the string correspond to consecutive boxes 0, 1, 2, .... The digit 0 means there is a red ball in the box, 1 means there is a green ball in the box, and 2 represents an empty box.

Examples

Input 1

10
0110220101

Output 1

5
1
3
5
8
2