Problem Statement

The country of yuki has $N$ towns numbered $1, 2, \ldots , N$ and $M$ roads numbered $1, 2, \ldots , M$. Road $i$ ($1\leq i\leq M$) connects town $a_i$ and town $b_i$. If $c_i=1$, road $i$ can be traversed in both directions; if $c_i=2$, road $i$ can only be traversed in the direction from town $a_i$ to town $b_i$.

Rusk is planning a sightseeing tour: he starts from some town, visits several towns by traveling along roads, and then returns to the original town. Here, he must visit at least $1$ town other than the starting town, and he wants to avoid visiting the same town twice (except for the final town) and traversing the same road twice. Determine whether this is possible.

Input

$N\ M$
$a_1\ b_1\ c_1$
$a_2\ b_2\ c_2$
$:$
$a_M\ b_M\ c_M$

• $2\leq N\leq 10^5$
• $1\leq M\leq 2\times 10^5$
• $1\leq a_i, b_i\leq N$
• $1\leq c_i\leq 2$
• $a_i\neq b_i$
• $a_i < b_i$ if $c_i=1$
• $(a_i, b_i, c_i)\neq (a_j, b_j, c_j)$ if $i\neq j$
• All input values are integers.

Output

Print Yes if it is possible to start from some town and return to the original town without passing through the same town or the same road twice, and No otherwise.

Sample

4 4
1 3 1
2 4 2
2 3 1
4 3 2

Yes

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

No

2 3
1 2 1
1 2 2
2 1 2

Yes

4 2
1 2 1
3 4 2

No