Square

Takahashi has an N \times N grid. The square at the i-th row and the j-th column of the grid is denoted by (i,j). Particularly, the top-left square of the grid is (1,1), and the bottom-right square is (N,N).

An integer, 0 or 1, is written on M of the squares in the Takahashi's grid. Three integers a_i,b_i and c_i describe the i-th of those squares with integers written on them: the integer c_i is written on the square (a_i,b_i).

Takahashi decides to write an integer, 0 or 1, on each of the remaining squares so that the condition below is satisfied. Find the number of such ways to write integers, modulo 998244353.

• For all 1\leq i < j\leq N, there are even number of 1s in the square region whose top-left square is (i,i) and whose bottom-right square is (j,j).

Constraints

• 2 \leq N \leq 10^5
• 0 \leq M \leq min(5 \times 10^4,N^2)
• 1 \leq a_i,b_i \leq N(1\leq i\leq M)
• 0 \leq c_i \leq 1(1\leq i\leq M)
• If i \neq j, then (a_i,b_i) \neq (a_j,b_j).
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M a_1 b_1 c_1 : a_M b_M c_M

Output

Print the number of possible ways to write integers, modulo 998244353.

Examples

Input

3 3 1 1 1 3 1 0 2 3 1

Output

8

Input

4 5 1 3 1 2 4 0 2 3 1 4 2 1 4 4 1

Output

32

Input

3 5 1 3 1 3 3 0 3 1 0 2 3 1 3 2 1

Output

0

Input

4 8 1 1 1 1 2 0 3 2 1 1 4 0 2 1 1 1 3 0 3 4 1 4 4 1

Output

4

Input

100000 0

Output

342016343

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N M a_1 b_1 c_1 : a_M b_M c_M

outputFormat

Output

Print the number of possible ways to write integers, modulo 998244353.

Examples

Input

3 3 1 1 1 3 1 0 2 3 1

Output

8

Input

4 5 1 3 1 2 4 0 2 3 1 4 2 1 4 4 1

Output

32

Input

3 5 1 3 1 3 3 0 3 1 0 2 3 1 3 2 1

Output

0

Input

4 8 1 1 1 1 2 0 3 2 1 1 4 0 2 1 1 1 3 0 3 4 1 4 4 1

Output

4

Input

100000 0

Output

342016343

样例

100000 0

342016343