A14004 | Correct Placement

Polycarp has invited $n$ friends to celebrate the New Year. During the celebration, he decided to take a group photo of all his friends. Each friend can stand or lie on the side.

Each friend is characterized by two values $h_i$ (their height) and $w_i$ (their width). On the photo the $i$ -th friend will occupy a rectangle $h_i \times w_i$ (if they are standing) or $w_i \times h_i$ (if they are lying on the side).

The $j$ -th friend can be placed in front of the $i$ -th friend on the photo if his rectangle is lower and narrower than the rectangle of the $i$ -th friend. Formally, at least one of the following conditions must be fulfilled:

- $h_j < h_i$ and $w_j < w_i$ (both friends are standing or both are lying);
- $w_j < h_i$ and $h_j < w_i$ (one of the friends is standing and the other is lying).

For example, if $n = 3$ , $h=[3,5,3]$ and $w=[4,4,3]$ , then:

- the first friend can be placed in front of the second: $w_1 < h_2$ and $h_1 < w_2$ (one of the them is standing and the other one is lying);
- the third friend can be placed in front of the second: $h_3 < h_2$ and $w_3 < w_2$ (both friends are standing or both are lying).

In other cases, the person in the foreground will overlap the person in the background.

Help Polycarp for each $i$ find any $j$ , such that the $j$ -th friend can be located in front of the $i$ -th friend (i.e. at least one of the conditions above is fulfilled).

Please note that you do not need to find the arrangement of all people for a group photo. You just need to find for each friend $i$ any other friend $j$ who can be located in front of him. Think about it as you need to solve $n$ separate independent subproblems.

The first line contains one integer $t$ ( $1 \leq t \leq 10^4$ ) — the number of test cases. Then $t$ test cases follow.

The first line of each test case contains one integer $n$ ( $1 \leq n \leq 2 \cdot 10^5$ ) — the number of friends.

This is followed by $n$ lines, each of which contains a description of the corresponding friend. Each friend is described by two integers $h_i$ and $w_i$ ( $1 \leq h_i, w_i \leq 10^9$ ) — height and width of the $i$ -th friend, respectively.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case output $n$ integers on a separate line, where the $i$ -th number is the index of a friend that can be placed in front of the $i$ -th. If there is no such friend, then output -1.

If there are several answers, output any.