A13680 | Finding Sasuke

Naruto has sneaked into the Orochimaru's lair and is now looking for Sasuke. There are $T$ rooms there. Every room has a door into it, each door can be described by the number $n$ of seals on it and their integer energies $a_1$ , $a_2$ , ..., $a_n$ . All energies $a_i$ are nonzero and do not exceed $100$ by absolute value. Also, $n$ is even.

In order to open a door, Naruto must find such $n$ seals with integer energies $b_1$ , $b_2$ , ..., $b_n$ that the following equality holds: $a_{1} \cdot b_{1} + a_{2} \cdot b_{2} + ... + a_{n} \cdot b_{n} = 0$ . All $b_i$ must be nonzero as well as $a_i$ are, and also must not exceed $100$ by absolute value. Please find required seals for every room there.

The first line contains the only integer $T$ ( $1 \leq T \leq 1000$ ) standing for the number of rooms in the Orochimaru's lair. The other lines contain descriptions of the doors.

Each description starts with the line containing the only even integer $n$ ( $2 \leq n \leq 100$ ) denoting the number of seals.

The following line contains the space separated sequence of nonzero integers $a_1$ , $a_2$ , ..., $a_n$ ( $|a_{i}| \leq 100$ , $a_{i} \neq 0$ ) denoting the energies of seals.

For each door print a space separated sequence of nonzero integers $b_1$ , $b_2$ , ..., $b_n$ ( $|b_{i}| \leq 100$ , $b_{i} \neq 0$ ) denoting the seals that can open the door. If there are multiple valid answers, print any. It can be proven that at least one answer always exists.