D. Recover the Treetime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputRhodoks has a tree with n vertices, but he doesn't remember its structure. The vertices are indexed from 1 to n.A segment [l,r] (1 \leq l \leq r \leq n) is good if the vertices with indices l, l + 1, ..., r form a connected component in Rhodoks' tree. Otherwise, it is bad.For example, if the tree is the one in the picture, then only the segment [3,4] is bad while all the other segments are good.  For each of the \frac{n(n+1)}{2} segments, Rhodoks remembers whether it is good or bad. Can you help him recover the tree? If there are multiple solutions, print any.It is guaranteed that the there is at least one tree satisfying Rhodoks' description. InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \leq t \leq 1000). The description of the test cases follows.The first line of each test case contains an integer n (1 \leq n \leq 2000) — the number of vertices in the tree.Then n lines follow. The i-th of these lines contains a string good_i of length n+1-i consisting of 0 and 1. If the segment [i,i+j-1] is good then the j-th character of good_i is 1, otherwise j-th character of good_i is 0.It is guaranteed that the there is at least one tree consistent with the given data. It is guaranteed that the sum of n over all test cases does not exceed 2000.OutputFor each test case, print n-1 lines describing the tree you recover. The i-th line should contain two integers u_i and v_i (1 \leq u_i,v_i \leq n), denoting an edge between vertices u_i and v_i.If there are multiple solutions, print any.ExampleInput
341111111101611111111111111111111112100100000001111000000011000000000100000000100100011110000100000100001001111101Output
1 2
2 3
2 4
1 2
2 3
3 4
4 5
5 6
2 3
6 7
10 11
2 4
6 8
10 12
1 4
5 8
9 12
5 12
2 12
NoteThe first test case is explained in the statement.In the second test case, one possible tree is as follows:  In the third test case, one possible tree is as follows:  
341111111101611111111111111111111112100100000001111000000011000000000100000000100100011110000100000100001001111101
1 2 2 3 2 4 1 2 2 3 3 4 4 5 5 6 2 3 6 7 10 11 2 4 6 8 10 12 1 4 5 8 9 12 5 12 2 12 
['constructive algorithms', 'trees', '*3400']