- 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 × N. Q of the entries of this matrix is 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, and Q.
- Each of the next Q lines contains 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 to the problem.

**Constraints**

1 ≤ T ≤ 10^6

2 ≤ N ≤ 10^5

1 ≤ Q ≤ 10^6

1 ≤ i, j ≤ N

0 ≤ val ≤ 1

The Sum of each of N, and Q over all test cases doesn’t exceed 106

**Sample Input 3:**

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

**Sample Output 3:**

`yes no yes no`

**Code:**

```
#include <iostream>
#include <vector>
#include<utility>
using namespace std;
const int N = 1e5 + 5;
bool error;
int col[N];
vector<pair<int, int>> adj[N];
void dfs(int start)
{
for (auto edge : adj[start])
{
int next = edge.first;
if (col[next] == -1)
{
col[next] = col[start] ^ edge.second;
dfs(next);
}
else if (col[next] != col[start] ^ edge.second)
{
error = true;
}
}
}
int main()
{
int t;
cin >> t;
while (t--)
{
int n, m;
cin >> n >> m;
error = false;
for (int i = 1; i <= n; i++)
{
adj[i].clear();
col[i] = -1;
}
while (m--)
{
int a, b, c;
cin >> a >> b >> c;
adj[a].push_back(make_pair(b, c));
adj[b].push_back(make_pair(a, c));
}
for (int i = 1; i <= n; i++)
{
if (col[i] == -1)
{
col[i] = 0;
dfs(i);
}
}
if (error)
cout << "no" << endl;
else
cout << "yes" << endl;
}
}
```

Code language: C++ (cpp)