The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other. Given an integer n, print all distinct solutions to the n-queens puzzle. Each solution contains distinct board configurations of the n-queens’ placement, where the solutions are a permutation of [1,2,3..n] in increasing order, here the number in the *ith* place denotes that the *ith*-column queen is placed in the row with that number. For eg below figure represents a chessboard [3 1 4 2].

**Input:**

The first line of input contains an integer T denoting the no of test cases. Then T test cases follow. Each test case contains an integer n denoting the size of the chessboard.

**Output:**

For each test case, output your solutions on one line where each solution is enclosed in square brackets '[', ']' separated by a space . The solutions are permutations of {1, 2, 3 …, *n*} in increasing order where the number in the ith place denotes the ith-column queen is placed in the row with that number, if no solution exists print -1.

**Constraints:**

1<=T<=10

1<=n<=10

**Example:
Input**

2

1

4

[1 ]

[2 4 1 3 ] [3 1 4 2 ]

DhruvKulshreshtha | 102 |

Radhaakrishna | 64 |

Mr_Bean | 58 |

Rishabh Jain 32 | 58 |

PRATEEK JAIN 16 | 57 |

Mr_Bean | 783 |

Dhirendra121 | 462 |

kinetic | 360 |

kevinyu102589 | 358 |

Guru_console | 330 |

akhayrutdinov | 4926 |

Ibrahim Nash | 4448 |

Quandray | 4261 |

sanjay05 | 3668 |

GB11 | 2857 |

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