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## HS11SEQ - Sequences

Given a positive integer n, please find all sequences of positive integers x1, x2, ..., xk such that the sum of all k elements of the above sequence is equal to n and for each i, 1<=i<k we have xi+1-xi in {-2, 0, 3}.

### Input

The first line contains the number of test cases t. Each of the following t lines contains just one number 1<=n<=30.

### Output

For each test case print all possible sequences satisfying the problem criteria. Sequences must be given in the lexicographic order, with each sequence printed in a separate line.

### Example

```Input:
4
2
3
4
8

Output:
1 1
2

1 1 1
3

1 1 1 1
2 2
3 1
4

1 1 1 1 1 1 1 1
1 1 1 1 4
1 1 4 2
2 2 2 2
3 1 1 1 1 1
3 1 4
3 3 1 1
4 2 2
4 4
5 3
8
```

### Scoring

By solving this problem you score 10 points.

 Added by: kuszi Date: 2012-01-15 Time limit: 1s-1.875s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM32-GCC ASM64 GAWK MAWK BC C-CLANG CPP14 CPP14-CLANG COBOL COFFEE D-CLANG D-DMD DART ELIXIR FANTOM FORTH GOSU GRV JS-MONKEY KTLN NIM NODEJS OBJC OBJC-CLANG OCT PICO PROLOG PYPY PY_NBC R RACKET RUST CHICKEN SED SQLITE SWIFT UNLAMBDA VB.NET Resource: High School Programming League