input:

361
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
2 10
2 11
2 12
2 13
2 14
2 15
2 16
2 17
2 18
2 19
2 20
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
3 10
3 11
3 12
3 13
3 14
3 15
3 16
3 17
3 18
3 19
3 20
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
4 10
4 11
4 12
4 13
4 14
4 15
4 16
4 17
4 18
4 19
4 20
5 2
5 3
5 4
5 5
5 6
5 7
5 8
5 9
5 1...

output:

4
11
11
6
111
111
6
1110
1101
8
11101
11011
10
111011
110111
11
1110111
1101110
12
11101110
11011101
14
111011101
110111011
16
1110111011
1101110111
17
11101110111
11011101110
18
111011101110
110111011101
20
1110111011101
1101110111011
22
11101110111011
11011101110111
23
111011101110111
110111011101...

result:

wrong answer 1s are not connected. (test case 3)