You are given an undirected graph with $n$ vertices, labeled from $1$ to $n$. This graph encodes a hidden permutation$^{\text{∗}}$ $p$ of size $n$. The graph is constructed as follows:

• For every pair of integers $1 \le i < j \le n$, an undirected edge is added between vertex $p_i$ and vertex $p_j$ if and only if $p_i < p_j$. Note that the edge is not added between vertices $i$ and $j$, but between the vertices of their respective elements. Refer to the notes section for better understanding.

Your task is to reconstruct and output the permutation $p$. It can be proven that permutation $p$ can be uniquely determined.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1 \le n \le 1000$).

The $i$-th of the next $n$ lines contains a string of $n$ characters $g_{i, 1}g_{i, 2}\ldots g_{i, n}$ ($g_{i, j} = \mathtt{0}$ or $g_{i, j} = \mathtt{1}$) — the adjacency matrix. $g_{i, j} = \mathtt{1}$ if and only if there is an edge between vertex $i$ and vertex $j$.

It is guaranteed that there exists a permutation $p$ which generates the given graph. It is also guaranteed that the graph is undirected and has no self-loops, meaning $g_{i, j} = g_{j, i}$ and $g_{i, i} = \mathtt{0}$.

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

Output

For each test case, output $n$ integers $p_1, p_2, \ldots, p_n$ representing the reconstructed permutation.

见题面 Input 部分

见题面 Output 部分

In the first case $p = [1]$. Since there are no pairs $1 \le i < j \le n$, there are no edges in the graph.

The graph in the second case is shown below. For example, when we choose $i = 3$ and $j = 4$, we add an edge between vertices $p_i = 1$ and $p_j = 3$, because $p_i < p_j$. However, when we choose $i = 2$ and $j = 3$, $p_i = 2$ and $p_j = 1$, so $p_i < p_j$ doesn't hold. Therefore, we don't add an edge between $2$ and $1$.

In the third case, there are no edges in the graph, so there are no pairs of integers $1 \le i < j \le n$ such that $p_i < p_j$. Therefore, $p = [6, 5, 4, 3, 2, 1]$.