Problem Statement

Takahashi and Aoki will play a game against each other using cards in three colors: red, green, and blue.

Initially, Takahashi has $R_1$ red, $G_1$ green, and $B_1$ blue cards, and Aoki has $R_2$ red, $G_2$ green, and $B_2$ blue cards in their hands. Each player knows the hands of both players. The game starts with Takahashi on offense and Aoki on defense, and repeats the process below.

1. First, the player on offense plays an arbitrary card from his hand.
2. Then, the player on defense either plays a card with the same color from his hand, or does nothing. If a card is played, the players switch between offense and defense.

The first player to have zero cards in his hand wins the game. Determine the winner when both players adopt the optimal strategy for their own victory.

For each input file, solve $T$ independent test cases.

Constraints

• $1 \leq T \leq 10^5$
• $0 \leq R_1, G_1, B_1, R_2, G_2, B_2 \leq 10^{18}$
• $R_1 + G_1 + B_1 \geq 1$
• $R_2 + G_2 + B_2 \geq 1$
• All values in the input are integers.

Input

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

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

Each test case is in the following format:

R_1 G_1 B_1 R_2 G_2 B_2

Output

For each test case, print Takahashi if Takahashi wins, and Aoki if Aoki wins.