Problem Statement

There is an $N \times N$ grid. Here, $N$ is even.

Determine whether it is possible to write either $0,1$ in each cell so that all of the following conditions are satisfied, and if it is possible, show one way to do so.

• For $i = 1,2,\ldots ,N$, the Hamming distance between the $i$-th row from the top and the $i + 1$-th row is $A$.
• For $i = 1,2,\ldots ,N$, the Hamming distance between the $i$-th column from the left and the $i + 1$-th column is $B$.

Here, the $N+1$-th row and the $N + 1$-th column refer to the $1$-st row and the $1$-st column, respectively.

There are $T$ test cases in total.

Constraints

• $1 \le T \le 1000$
• $2\le N \le 500$
• $N$ is even
• The sum of $N^2$ over all test cases is at most $250000$
• $0 \le A,B \le N$
• All input values are integers

Input

The input is given from standard input in the following format. Here, $\mathrm{case}_i$ is the $i$-th test case.

$T$
$\text{case}_1$
$\text{case}_2$
$\vdots$
$\text{case}_T$

Each test case is given in the following format.

$N\ A\ B$

Output

Print the answers to the test cases, separated by newlines.

If it is impossible to write the digits so that the conditions are satisfied, print $-1$. Otherwise, print one such way of writing them as $N$ lines of strings $S_1,\ldots,S_N$ of length $N$ consisting of $0,1$, separated by newlines.

Here, the $j$-th character of $S_{i}$ must be the character written in the cell at the $i$-th row from the top and the $j$-th column from the left.

If there are multiple ways of writing that satisfy the conditions, any of them will be accepted.

Sample

3
2 1 1
6 0 6
314 15 92

10
00
010101
010101
010101
010101
010101
010101
-1