Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Flights

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLiLand is a country, consisting of *n* cities. The cities are numbered from 1 to *n*. The country is well known because it has a very strange transportation system. There are many one-way flights that make it possible to travel between the cities, but the flights are arranged in a way that once you leave a city you will never be able to return to that city again.

Previously each flight took exactly one hour, but recently Lily has become the new manager of transportation system and she wants to change the duration of some flights. Specifically, she wants to change the duration of some flights to exactly 2 hours in such a way that all trips from city 1 to city *n* take the same time regardless of their path.

Your task is to help Lily to change the duration of flights.

Input

First line of the input contains two integer numbers *n* and *m* (2 ≤ *n* ≤ 1000; 1 ≤ *m* ≤ 5000) specifying the number of cities and the number of flights.

Each of the next *m* lines contains two integers *a*_{i} and *b*_{i} (1 ≤ *a*_{i} < *b*_{i} ≤ *n*) specifying a one-directional flight from city *a*_{i} to city *b*_{i}. It is guaranteed that there exists a way to travel from city number 1 to city number *n* using the given flights. It is guaranteed that there is no sequence of flights that forms a cyclical path and no two flights are between the same pair of cities.

Output

If it is impossible for Lily to do her task, print "No" (without quotes) on the only line of the output.

Otherwise print "Yes" (without quotes) on the first line of output, then print an integer *ans*_{i} (1 ≤ *ans*_{i} ≤ 2) to each of the next *m* lines being the duration of flights in new transportation system. You should print these numbers in the order that flights are given in the input.

If there are multiple solutions for the input, output any of them.

Examples

Input

3 3

1 2

2 3

1 3

Output

Yes

1

1

2

Input

4 4

1 2

2 3

3 4

1 4

Output

No

Input

5 6

1 2

2 3

3 5

1 4

4 5

1 3

Output

Yes

1

1

1

2

1

2

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/30/2017 04:17:19 (c4).

Desktop version, switch to mobile version.
User lists

Name |
---|