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

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