Circles Intersection

You are given circle $A$ with radius $r_a$ and with central coordinate $(x_a, y_a)$ and circle $B$ with radius $r_b$ and with central coordinate $(x_b, y_b)$.

Write a program which prints:

• "2" if $B$ is in $A$,
• "-2" if $A$ is in $B$,
• "1" if circumference of $A$ and $B$ intersect, and
• "0" if $A$ and $B$ do not overlap.

You may assume that $A$ and $B$ are not identical.

Input

The input consists of multiple datasets. The first line consists of an integer $N$ ($N \leq 50$), the number of datasets. There will be $N$ lines where each line represents each dataset. Each data set consists of real numbers:

$x_a$ $y_a$ $r_a$ $x_b$ $y_b$ $r_b$

Output

For each dataset, print 2, -2, 1, or 0 in a line.

Example

Input

2 0.0 0.0 5.0 0.0 0.0 4.0 0.0 0.0 2.0 4.1 0.0 2.0

Output

2 0

inputFormat

Input

The input consists of multiple datasets. The first line consists of an integer $N$ ($N \leq 50$), the number of datasets. There will be $N$ lines where each line represents each dataset. Each data set consists of real numbers:

$x_a$ $y_a$ $r_a$ $x_b$ $y_b$ $r_b$

outputFormat

Output

For each dataset, print 2, -2, 1, or 0 in a line.

Example

Input

2 0.0 0.0 5.0 0.0 0.0 4.0 0.0 0.0 2.0 4.1 0.0 2.0

Output

2 0

样例

2
0.0 0.0 5.0 0.0 0.0 4.0
0.0 0.0 2.0 4.1 0.0 2.0

2
0

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