AdoraBalls

An orphanage nearby collects a cheap toy ball called an AdoraBall. AdoraBalls come in four colours: azure, blue, cyan, and denim. Nobody sells them one at a time. The only thing you can buy is one of these four bundles.

• One Bundle of Enjoyment holds $a_1$ azure balls, $b_1$ blue balls, $c_1$ cyan balls, and $d_1$ denim balls.
• One Bundle of Festivity holds $a_2$ azure balls, $b_2$ blue balls, $c_2$ cyan balls, and $d_2$ denim balls.
• One Bundle of Glee holds $a_3$ azure balls, $b_3$ blue balls, $c_3$ cyan balls, and $d_3$ denim balls.
• One Bundle of Happiness holds $a_4$ azure balls, $b_4$ blue balls, $c_4$ cyan balls, and $d_4$ denim balls.

Every child in the orphanage has exactly one favourite colour among the four. $a_0$ children like azure best, $b_0$ like blue best, $c_0$ like cyan best, and $d_0$ like denim best.

You buy $E$ Bundles of Enjoyment, $F$ Bundles of Festivity, $G$ Bundles of Glee, and $H$ Bundles of Happiness, where $E$, $F$, $G$, $H$ are non-negative integers. Then you open every bundle you bought and hand out the balls under three rules.

• A child receives balls of their own favourite colour only.
• Every child receives the same number of balls, and that number is at least one.
• No ball is left over. You keep none of them.

Decide whether some choice of $E$, $F$, $G$, $H$ obeys all three rules.

If the orphanage has no children at all, buying nothing obeys all three rules, so the answer is yes.

The first line holds one integer $T$, the number of test cases.

Each test case takes five lines. The first line holds four integers $a_0$, $b_0$, $c_0$, $d_0$, the number of children whose favourite colour is azure, blue, cyan, and denim, in that order. Line $i$ of the next four lines holds $a_i$, $b_i$, $c_i$, $d_i$, the contents of the $i$-th bundle.

Constraints

• $1 \le T \le 20000$
• $0 \le a_i, b_i, c_i, d_i \le 55$ for every $i = 0, 1, 2, 3, 4$

For each test case, print one line. Print POSSIBALL if non-negative integers $E$, $F$, $G$, $H$ obeying all three rules exist, and IMPOSSIBALL otherwise.