You are given a binary matrix $$$b$$$ (all elements of the matrix are $$$0$$$ or $$$1$$$) of $$$n$$$ rows and $$$n$$$ columns.

You need to construct a $$$n$$$ sets $$$A_1, A_2, \ldots, A_n$$$, for which the following conditions are satisfied:

Each set is nonempty and consists of distinct integers between $$$1$$$ and $$$n$$$ inclusive.
All sets are distinct.
For all pairs $$$(i,j)$$$ satisfying $$$1\leq i, j\leq n$$$, $$$b_{i,j}=1$$$ if and only if $$$A_i\subsetneq A_j$$$. In other words, $$$b_{i, j}$$$ is $$$1$$$ if $$$A_i$$$ is a proper subset of $$$A_j$$$ and $$$0$$$ otherwise.

Set $$$X$$$ is a proper subset of set $$$Y$$$, if $$$X$$$ is a nonempty subset of $$$Y$$$, and $$$X \neq Y$$$.

It's guaranteed that for all test cases in this problem, such $$$n$$$ sets exist. Note that it doesn't mean that such $$$n$$$ sets exist for all possible inputs.

If there are multiple solutions, you can output any of them.

Input

Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1\le t\le 1000$$$) — the number of test cases. The description of test cases follows.

The first line contains a single integer $$$n$$$ ($$$1\le n\le 100$$$).

The following $$$n$$$ lines contain a binary matrix $$$b$$$, the $$$j$$$-th character of $$$i$$$-th line denotes $$$b_{i,j}$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$1000$$$.

It's guaranteed that for all test cases in this problem, such $$$n$$$ sets exist.

Output

For each test case, output $$$n$$$ lines.

For the $$$i$$$-th line, first output $$$s_i$$$ $$$(1 \le s_i \le n)$$$ — the size of the set $$$A_i$$$. Then, output $$$s_i$$$ distinct integers from $$$1$$$ to $$$n$$$ — the elements of the set $$$A_i$$$.

If there are multiple solutions, you can output any of them.

It's guaranteed that for all test cases in this problem, such $$$n$$$ sets exist.

Note

In the first test case, we have $$$A_1 = \{1, 2, 3\}, A_2 = \{1, 3\}, A_3 = \{2, 4\}, A_4 = \{1, 2, 3, 4\}$$$. Sets $$$A_1, A_2, A_3$$$ are proper subsets of $$$A_4$$$, and also set $$$A_2$$$ is a proper subset of $$$A_1$$$. No other set is a proper subset of any other set.

In the second test case, we have $$$A_1 = \{1\}, A_2 = \{1, 2\}, A_3 = \{1, 2, 3\}$$$. $$$A_1$$$ is a proper subset of $$$A_2$$$ and $$$A_3$$$, and $$$A_2$$$ is a proper subset of $$$A_3$$$.

Set Construction

Examples