People on a Line

There are N people standing on the x-axis. Let the coordinate of Person i be x_i. For every i, x_i is an integer between 0 and 10^9 (inclusive). It is possible that more than one person is standing at the same coordinate.

You will given M pieces of information regarding the positions of these people. The i-th piece of information has the form (L_i, R_i, D_i). This means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.

It turns out that some of these M pieces of information may be incorrect. Determine if there exists a set of values (x_1, x_2, ..., x_N) that is consistent with the given pieces of information.

Constraints

• 1 \leq N \leq 100 000
• 0 \leq M \leq 200 000
• 1 \leq L_i, R_i \leq N (1 \leq i \leq M)
• 0 \leq D_i \leq 10 000 (1 \leq i \leq M)
• L_i \neq R_i (1 \leq i \leq M)
• If i \neq j, then (L_i, R_i) \neq (L_j, R_j) and (L_i, R_i) \neq (R_j, L_j).
• D_i are integers.

Input

Input is given from Standard Input in the following format:

N M L_1 R_1 D_1 L_2 R_2 D_2 : L_M R_M D_M

Output

If there exists a set of values (x_1, x_2, ..., x_N) that is consistent with all given pieces of information, print Yes; if it does not exist, print No.

Examples

Input

3 3 1 2 1 2 3 1 1 3 2

Output

Yes

Input

3 3 1 2 1 2 3 1 1 3 5

Output

No

Input

4 3 2 1 1 2 3 5 3 4 2

Output

Yes

Input

10 3 8 7 100 7 9 100 9 8 100

Output

No

Input

100 0

Output

Yes

inputFormat

Input

Input is given from Standard Input in the following format:

N M L_1 R_1 D_1 L_2 R_2 D_2 : L_M R_M D_M

outputFormat

Output

If there exists a set of values (x_1, x_2, ..., x_N) that is consistent with all given pieces of information, print Yes; if it does not exist, print No.

Examples

Input

3 3 1 2 1 2 3 1 1 3 2

Output

Yes

Input

3 3 1 2 1 2 3 1 1 3 5

Output

No

Input

4 3 2 1 1 2 3 5 3 4 2

Output

Yes

Input

10 3 8 7 100 7 9 100 9 8 100

Output

No

Input

100 0

Output

Yes

样例

3 3
1 2 1
2 3 1
1 3 5

No