Roger has taken ~N~ tests in preparation for CCO. On each test, there were a total of ~b_i~ marks available and Roger got ~a_i~ marks. Roger's final score is ~\frac{\sum_i a_i}{\sum_i b_i}~. Roger's test percentages are all distinct.

Roger's teacher decides that, for some value of ~D~, Roger's ~D~ lowest percentages will be dropped in evaluating his final score. Roger discovers that it may be possible to select a different set of ~D~ tests to drop which will result in a strictly higher score. Compute all ~D~ such that this is the case.

Constraints

~1 \le N \le 5 \cdot 10^4~

~0 \le a_i \le b_i < 4 \cdot 10^4~

~b_i > 0~

Input Specification

The first line will contain an integer ~N~.

Each of the next ~N~ lines will contain two integers, ~a_i~ and ~b_i~.

Output Specification

Output ~K+1~ lines. On the first line, output ~K~. On each of the next ~K~ lines, in ascending order, print the values of ~D~ for which Roger can do better than his teacher in maximizing his score. All valid values of ~D~ must be generated.

Sample Input

5
1 2
5 9
3 8
4 10
1 3

Sample Output

2
1
2