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
1101
1110
8
11011
11101
10
110111
111011
11
1101110
1110111
12
11011101
11101110
14
110111011
111011101
16
1101110111
1110111011
17
11011101110
11101110111
18
110111011101
111011101110
20
1101110111011
1110111011101
22
11011101110111
11101110111011
23
110111011101110
111011101110...

result:

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