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