Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

3 3
1 2 1
2 3 1
1 3 2

Sample Output 1

Yes

Some possible sets of values (x_1, x_2, x_3) are (0, 1, 2) and (101, 102, 103).

Sample Input 2

3 3
1 2 1
2 3 1
1 3 5

Sample Output 2

No

If the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.

Sample Input 3

4 3
2 1 1
2 3 5
3 4 2

Sample Output 3

Yes

Sample Input 4

10 3
8 7 100
7 9 100
9 8 100

Sample Output 4

No

Sample Input 5

100 0

Sample Output 5

Yes

Solution in Perl (v5.18.2) (judge verdict: Runtime Error)

($N,$M) =split(" ",<STDIN>);
for($i=0;$i<$M;$i++) {
	($L,$R,$D)=split(" ",<STDIN>);
	$L--;$R--;
	push @L,$L;
	push @R,$R;
	push @D,$D;
	$C{$L}{$R}=$#D;
	$C{$R}{$L}=$#D;
}

$m=0;
while ($m<$M) {
	$M{$m}=1;
	push @M,$m;
	$L=$L[$m];$R=$R[$m];
	push @K,$L;$K{$L}=1;
	push @K,$R;$K{$R}=1;
	$x{$L} = 0;
	$x{$R} = $D[$m];
	
	while ($#K>=0){
		$i=pop(@K);
		foreach $j ( keys %{$C{$i}} ) {
			$n=$C{$i}{$j};
			next if ($M{$n});
			$M{$n}=1;
			push @M,$n;
			if (!exists($K{$j})) {
				push @K,$j;$K{$j}=1;
			}
		}
	}
	$m++;
	for(;$M{$m}!=0;$m++){}
}

for($i=0;$i<=$#M;$i++){
	$m=$M[$i];$L=$L[$m];$R=$R[$m];
	if ( exists($x{$L}) ) {
		if ( exists($x{$R}) ) {
			if ($x{$R} != $x{$L}+$D[$m]) {
				print "No";
				goto exit1;
			}
		} else {
			$x{$R} = $x{$L}+$D[$m];
		}
	} else {
		$x{$L} = $x{$R}-$D[$m];
	}
}