DreamGrid has $n$ classmates numbered from $1$ to $n$. Some of them are boys and the others are girls. Each classmate has some gems, and more specifically, the $i$-th classmate has $i$ gems.

DreamGrid would like to divide the classmates into four groups $G_1$, $G_2$, $G_3$ and $G_4$ such that:

Each classmate belongs to exactly one group.

Both $G_1$ and $G_2$ consist only of girls. Both $G_3$ and $G_4$ consist only of boys.

The total number of gems in $G_1$ and $G_3$ is equal to the total number of gems in $G_2$ and $G_4$.

Your task is to help DreamGrid group his classmates so that the above conditions are satisfied. Note that you are allowed to leave some groups empty.

There are multiple test cases. The first line of input is an integer $T$ indicating the number of test cases. For each test case:

The first line contains an integer $n$ ($1 \le n \le 10^5$) -- the number of classmates.

The second line contains a string $s$ ($|s| = n$) consisting of 0 and 1. Let $s_i$ be the $i$-th character in the string $s$. If $s_i = 1$, the $i$-th classmate is a boy; If $s_i = 0$, the $i$-th classmate is a girl.

It is guaranteed that the sum of all $n$ does not exceed $10^6$.

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