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