### Problem Statement

There are N people standing on the x-axis. Let the coordinate of Person i be xi. For every i, xi is an integer between 0 and 109 (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 (Li, Ri, Di). This means that Person Ri is to the right of Person Li by Di units of distance, that is, xRi - xLi = Di holds.

It turns out that some of these M pieces of information may be incorrect. Determine if there exists a set of values (x1, x2, ..., xN) that is consistent with the given pieces of information.

### Constraints

• 1 ≤ N ≤ 100 000
• 0 ≤ M ≤ 200 000
• 1 ≤ Li, Ri ≤ N (1 ≤ i ≤ M)
• 0 ≤ Di ≤ 10 000 (1 ≤ i ≤ M)
• Li ≠ Ri (1 ≤ i ≤ M)
• If i ≠ j, then (Li, Ri) ≠ (Lj, Rj) and (Li, Ri) ≠ (Rj, Lj).
• Di are integers.

### Input

Input is given from Standard Input in the following format:

```N M
L1 R1 D1
L2 R2 D2
:
LM RM DM
```

### Output

If there exists a set of values (x1, x2, ..., xN) that is consistent with all given pieces of information, print `Yes`; if it does not exist, print `No`.

```3 3
1 2 1
2 3 1
1 3 2
```

### Sample Output 1

```Yes
```

Some possible sets of values (x1, x2, x3) are (0, 1, 2) and (101, 102, 103).

```3 3
1 2 1
2 3 1
1 3 5
```

### Sample Output 2

```No
```

If the first two pieces of information are correct, x3 - x1 = 2 holds, which is contradictory to the last piece of information.

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

```Yes
```

```10 3
8 7 100
7 9 100
9 8 100
```

```No
```

```100 0
```

```Yes
```