Fruits

Task

You are given $N$ baskets. The $i$-th basket contains $A_i$ apples, $B_i$ bananas and $C_i$ cherries. Pick at most $\left\lfloor\frac{N+3}{2}\right\rfloor$ baskets in a way that you get at least half of each fruit.

It can be proven that there is always a solution. If there are multiple solutions, you can output any of them.

Input data

The first line of the input file contains a single integer $T$, the number of test cases. $T$ test cases follow.

Each test case consists of:

• a line containing integer $N$, the number of baskets.
• $N$ lines, the $i$-th of which consisting of integers $A_i$, $B_i$, $C_i$, the number of apples, bananas, cherries in the $i$-th basket.

Output data

The output file must contain $2 \cdot T$ lines, two lines for each test case. For each test case:

• Print a single integer $M \le \left\lfloor \frac{N+3}{2} \right\rfloor$, the number of baskets you choose.
• On the next line, print $M$ integers $R_0, R_1, \dots, R_{M-1}$ -- the 0-based indices of the chosen baskets, separated by spaces.

Constraints and clarifications

• $1 \le T \le 1 \ 000$.
• $2 \le N \le 1 \ 000$. It is guaranteed that the sum of $N$ over all test cases does not exceed $1 \ 000 \ 000$.
• $0 \le A_i, B_i, C_i \le 1 \ 000 \ 000$ for each $i=0\ldots N-1$.

Example 1

stdin

1
6
1 0 0
1 0 0
1 0 0
0 1 0
0 1 0
0 0 2

stdout

4
0 1 3 5

Explanation

In the first sample case, we need at least half of each fruit:

• Apples $\ge$ 2 $\to$ pick at least 2 baskets from first 3 (1 0 0)
• Bananas $\ge$ 1 $\to$ pick at least 1 basket from baskets 3-4 (0 1 0)
• Cherries $\ge$ 1 $\to$ pick basket 5 (0 0 2)

Example 2

stdin

1
6
6 1 2
1 6 2
2 2 5
1 2 6
3 3 3
2 2 4

stdout

4
0 1 2 3