# CodeChef : September Challenge 2017 – Fill The Matrix

By | September 10, 2017

#### Fill The Matrix

Source: CodeChef

Fill The Matrix : A matrix B (consisting of integers) of dimension N × N is said to be good if there exists an array A (consisting of integers) such that B[i][j] = |A[i] – A[j]|, where |x| denotes absolute value of integer x.

You are given a partially filled matrix B of dimension N × NQ of the entries of this matrix are filled by either 0 or 1. You have to identify whether it is possible to fill the remaining entries of matrix B (the entries can be filled by any integer, not necessarily by 0 or 1) such that the resulting fully filled matrix B is good.

### Input

The first line of the input contains an integer T denoting the number of test cases.

The first line of each test case contains two space separated integers N, Q.

Each of the next Q lines contain three space separated integers i, j, val, which means that B[i][j] is filled with value val.

### Output

For each test case, output “yes” or “no” (without quotes) in a single line corresponding to the answer of the problem.

### Constraints

• 1 ≤ T ≤ 106
• 2 ≤ N ≤ 105
• 1 ≤ Q ≤ 106
• 1 ≤ i, j ≤ N
• 0 ≤ val ≤ 1
• Sum of each of N, Q over all test cases doesn’t exceed 106

• Subtask #1 (40 points) 2 ≤ N ≤ 103, 1 ≤ Q ≤ 103, Sum of each of N, Q over all test cases doesn’t exceed 104
• Subtask #2 (60 points) Original Constraints

```Input
4
2 2
1 1 0
1 2 1
2 3
1 1 0
1 2 1
2 1 0
3 2
2 2 0
2 3 1
3 3
1 2 1
2 3 1
1 3 1

Output
yes
no
yes
no
```

### Explanation

Example 1. You can fill the entries of matrix B as follows.

```0 1
1 0
```

This matrix corresponds to the array A = [1, 2].

Example 2. It is impossible to fill the remaining entries of matrix B such that the resulting matrix is good, as B[1][2] = 1 and B[2][1] = 0, which is impossible.

### Solution

`Working on the Solution`