Description

There are N animals standing in line.

The strength of the i-th animal is s_i and the height of the i-th animal is h_i.

The i-th animal is said to be better than the j-th animal if （s_i > s_j） or （s_i = s_j and h_i > h_j）.

For each i = 1, 2, ..., N, find the largest j such that j < i and the j-th animal is better than the i-th animal.

 

Input

The first line of the input contains an integer T, the number of testcases.

The first line of each testcase contains an integer N, the number of animals.

The second line of each testcase contains N integers, s₁, s₂, ..., s_N, the strength of animals.

The third line of each testcase contains N integers, h₁, h₂, ..., h_N, the height of animals.

 

For test 1 to 3, N <= 10³.

For test 4 to 6, N <= 10⁵.

T <= 10, s_i,  h_i <= 10⁹.

 

Output

For each testcase, please print N integers j₁, j₂, ..., j_N seperated by space.

j_i represent the largest number such that j_i < i and the j_i-th animal is better than the i-th animal.

If such j_i doesn't exist, print 0 instead.

Remember to print a new line at the end of each line.

 

Sample Input  Download

Sample Output  Download

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