I. Physical Examinationtime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputPolycarp plans to undergo a full physical examination at his local clinic. There are n doctors, numbered from 1 to n. The i-th doctor takes patients from minute L_i to minute R_i, so Polycarp can visit him at any minute in this range. It takes each doctor exactly one minute to examine Polycarp's health.Polycarp wants to arrive at the clinic at some minute x and visit all n doctors in some order without waiting or visiting any doctor several times.More formally, he chooses an integer x and a permutation p_1, p_2, \dots, p_n (a sequence of n integers from 1 to n such that each integer appears exactly once), then proceeds to visit:   doctor p_1 at minute x;  doctor p_2 at minute x+1;  ...  doctor p_n at minute x+n-1. The p_i-th doctor should be able to take patients at minute x+i-1, so the following should hold: L[p_i] \le x + i - 1 \le R[p_i].Determine if it's possible for Polycarp to choose such a minute x and a permutation p that he'll be able to visit all n doctors in without waiting or visiting any doctor several times. If there are multiple answers, print any of them.InputThe first line contains a single integer t (1 \le t \le 100) — the number of testcases.Then the descriptions of t testcases follow.The first line of the testcase contains a single integer n (1 \le n \le 10^5) — the number of doctors.The second line of the testcase contains n integers L_1, L_2, \dots L_n (1 \le L_i \le 10^9).The third line of the testcase contains n integers R_1, R_2, \dots R_n (L_i \le R_i \le 10^9).The sum of n over all testcases doesn't exceed 10^5.OutputFor each testcase print an answer.If there exists such a minute x and a permutation p that Polycarp is able to visit all n doctors without waiting or visiting any doctor several times, then print x in the first line and a permutation p in the second line. If there are multiple answers, print any of them.Otherwise, print -1 in the only line.ExampleInput
5
3
2 3 1
3 3 2
8
6 6 5 4 9 4 3 6
7 6 10 6 9 6 6 8
2
4 2
4 2
3
2 2 2
3 3 3
1
5
10
Output
1
3 1 2 
3
7 4 6 2 1 8 5 3 
-1
-1
7
1 
NoteIn the third testcase it's impossible to visit all doctors, because Polycarp has to visit doctor 2 at minute 2 and doctor 1 at minute 4. However, that would require him to wait a minute between the visits, which is not allowed.In the fourth testcase all doctors take patients in the span of 2 minutes. However, since there are three of them, Polycarp can't visit them all.
5
3
2 3 1
3 3 2
8
6 6 5 4 9 4 3 6
7 6 10 6 9 6 6 8
2
4 2
4 2
3
2 2 2
3 3 3
1
5
10

1 3 1 2  3 7 4 6 2 1 8 5 3  -1 -1 7 1  
['*special problem', 'binary search', 'data structures', '*3200']