Magic Square

A magic square is an $N \times N$ matrix that satisfies the following three conditions.

1. Every entry is an integer between $1$ and $N^2$.
2. All entries are distinct.
3. The $N$ row sums, the $N$ column sums, and the two diagonal sums are all equal.

The following $3 \times 3$ matrix is a magic square.

The row sums are 8+3+4, 1+5+9, 6+7+2, the column sums are 8+1+6, 3+5+7, 4+9+2, and the two diagonal sums are 8+5+2 and 4+5+6. All eight sums equal 15.

You are given an $N \times N$ matrix with some of its entries already filled in. Decide whether the empty entries can be filled so that the matrix becomes a magic square.

The first line contains the size of the matrix $N$ ($2 \le N \le 5$) and the number of filled entries $E$ ($0 \le E \le N^2$), separated by a space.

Each of the next $E$ lines contains the row index $R$ ($1 \le R \le N$), the column index $C$ ($1 \le C \le N$), and the value $V$ ($1 \le V \le N^2$) of one filled entry, separated by spaces. All the values $V$ are distinct.

Print yes if the given matrix can be completed into a magic square, and no otherwise.