Xor Battle

There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):

• Person S_i does one of the following:
• Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
• Do nothing.

Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.

Determine whether x becomes 0 at the end of the game when the two persons play optimally.

Solve T test cases for each input file.

Constraints

• 1 \leq T \leq 100
• 1 \leq N \leq 200
• 1 \leq A_i \leq 10^{18}
• S is a string of length N consisting of 0 and 1.
• All numbers in input are integers.

Input

Input is given from Standard Input in the following format. The first line is as follows:

T

Then, T test cases follow. Each test case is given in the following format:

N A_1 A_2 \cdots A_N S

Output

For each test case, print a line containing 0 if x becomes 0 at the end of the game, and 1 otherwise.

Example

Input

3 2 1 2 10 2 1 1 10 6 2 3 4 5 6 7 111000

Output

1 0 0

inputFormat

input file.

Constraints

• 1 \leq T \leq 100
• 1 \leq N \leq 200
• 1 \leq A_i \leq 10^{18}
• S is a string of length N consisting of 0 and 1.
• All numbers in input are integers.

Input

Input is given from Standard Input in the following format. The first line is as follows:

T

Then, T test cases follow. Each test case is given in the following format:

N A_1 A_2 \cdots A_N S

outputFormat

Output

For each test case, print a line containing 0 if x becomes 0 at the end of the game, and 1 otherwise.

Example

Input

3 2 1 2 10 2 1 1 10 6 2 3 4 5 6 7 111000

Output

1 0 0

样例

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000

1
0
0

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