# 2832. Zero

Let‘s consider the sequence of digits from 1 through N (where N=9) in increasing order: 1 2 3 … N. Now insert either a '+' for addition or a '-' for subtraction or a ' ' [blank] to run the digits together, between each pair of digits (not in front of the first digit). Calculate the result that of the expression and see if you get zero.

Write a program that will find all sequences of length N that produce a zero sum.

### 输入格式

The first line of the input contains the number of test cases (<10). Single test case is represented by single line that contains the integer N (3 <= N <= 9).

### 输出格式

For each test case in ASCII order, print each sequence that can create 0 sum with a '+', '-', or ' ' (space) between each pair of numbers. Space shows that the digits run together. Different test cases should be separated by an empty line.

### 样例

Input
2
3
7

Output
1+2-3
1+2-3+4-5-6+7
1+2-3-4+5+6-7
1-2 3+4+5+6+7
1-2 3-4 5+6 7
1-2+3+4-5+6-7
1-2-3-4-5+6+7


23 人解决，30 人已尝试。

26 份提交通过，共有 49 份提交。

4.2 EMB 奖励。