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line Batch , stdin/stdout

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line.html

Title

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.

Sample Input 1

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).

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, x3 - x1 = 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

Tags

Subtasks and Limits

Subtask Score #TC Time Memory Scoring
1100421s256MBMinimum
2051s256MBMinimum

Judge Compile Command

g++-8 ans.cpp -o line -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512

Accepted Submissions

subIDUserTimeMax Time

Past Submissions

subIDUserTimeScore
mrJudge 09.05.20
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