Problem Statement

The problem setting of this problem is partially shared with Problem A.

In the year $3333$, CatCoder will hold the CatCoder Triple Contest (abbreviated as C3C).

There are $N$ writers who have problem proposals. Each writer's problem proposals are classified into $5$ types by difficulty: Hell, Hard, Medium, Easy, Baby, and the $i$-th writer has $A_i,B_i,C_i,D_i,E_i$ problem proposals of Hell, Hard, Medium, Easy, Baby, respectively.

Each C3C simultaneously holds $3$ divisions, Div.1, Div.2, and Div.3. The problem proposals required for each division are as follows:

• Div.1: One Hell, one Hard, and one Medium problem proposal from the same writer
• Div.2: One Hard, one Medium, and one Easy problem proposal from the same writer
• Div.3: One Medium, one Easy, and one Baby problem proposal from the same writer

Note that the writers for Div.1, Div.2, and Div.3 do not necessarily have to be the same. Also, each problem proposal can be used in at most one division of one C3C.

For $k=1,2,\dots,N$, let $X_k$ be the maximum number of times C3C can be held using only the problem proposals of the first $k$ writers. Find $X_1,X_2,\dots ,X_N$.

$T$ test cases are given, so find the answer for each.

Constraints

• $1 \le T \le 10^5$
• $1 \le N \le 2 \times 10^5$
• $1 \le A_i,B_i,C_i,D_i,E_i \le 10^9$
• The sum of $N$ over all test cases is at most $2 \times 10^5$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\text{case}_1
\text{case}_2
\vdots
\text{case}_T

Each test case is given in the following format:

N
A_1 B_1 C_1 D_1 E_1
A_2 B_2 C_2 D_2 E_2
\vdots
A_N B_N C_N D_N E_N

Output

Output $T$ lines.

The $i$-th line should contain $X_1,X_2,\dots ,X_N$ separated by spaces for the $i$-th test case.