As this problem has been cloned as practice for someone(include me), we found that the standard code of the author of the mashup, zaozao_zmx1, is wrong.

liqingyang has been giving us several data for hacking, which is following:

hack 1:

1
15 7
13 14
14 6
11 8
7 13
11 9
1 7
8 15
5 2
9 6
3 1
10 3
4 15
15 12
3 5

hack 2:

1
15 8
8 2
3 4
8 12
3 12
3 1
9 7
3 11
15 2
7 11
13 9
6 15
7 14
6 10
5 14

And the correct answers of them are both 5, while almost half of the submissions give out wrong answers, such as3, 4 and 6.

The wrong codes have been ignored.

Update: another hack from Minion123, whose answer should be 4.

1
15 3
8 15
3 4
10 8
11 10
12 3
8 5
13 15
4 2
14 12
15 14
6 15
8 7
9 2
8 1

For the problem 1641D, I made a greedy solution. And in fact, it has passed the SYSTEM TEST!

However, I can't prove its correctness, so the threshold was estimated.

Can this code be hacked?

How can you hack it?

And how can the threshold be exactly chosen?