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
0111
8
11011
10111
9
111011
011101
11
1110111
0111011
12
11101110
01110111
14
110111011
101110111
15
1110111011
0111011101
17
11101110111
01110111011
18
111011101110
011101110111
20
1101110111011
1011101110111
21
11101110111011
01110111011101
23
111011101110111
0111011101110...

result:

wrong answer 1s are not connected. (test case 4)