Two Elevators
Description
Vlad went into his appartment house entrance, now he is on the $1$-th floor. He was going to call the elevator to go up to his apartment.
There are only two elevators in his house. Vlad knows for sure that:
- the first elevator is currently on the floor $a$ (it is currently motionless),
- the second elevator is located on floor $b$ and goes to floor $c$ ($b \ne c$). Please note, if $b=1$, then the elevator is already leaving the floor $1$ and Vlad does not have time to enter it.
If you call the first elevator, it will immediately start to go to the floor $1$. If you call the second one, then first it will reach the floor $c$ and only then it will go to the floor $1$. It takes $|x - y|$ seconds for each elevator to move from floor $x$ to floor $y$.
Vlad wants to call an elevator that will come to him faster. Help him choose such an elevator.
The first line of the input contains the only $t$ ($1 \le t \le 10^4$) — the number of test cases.
This is followed by $t$ lines, three integers each $a$, $b$ and $c$ ($1 \le a, b, c \le 10^8$, $b \ne c$) — floor numbers described in the statement.
Output $t$ numbers, each of which is the answer to the corresponding test case. As an answer, output:
- $1$, if it is better to call the first elevator;
- $2$, if it is better to call the second one;
- $3$, if it doesn't matter which elevator to call (both elevators will arrive in the same time).
Input
The first line of the input contains the only $t$ ($1 \le t \le 10^4$) — the number of test cases.
This is followed by $t$ lines, three integers each $a$, $b$ and $c$ ($1 \le a, b, c \le 10^8$, $b \ne c$) — floor numbers described in the statement.
Output
Output $t$ numbers, each of which is the answer to the corresponding test case. As an answer, output:
- $1$, if it is better to call the first elevator;
- $2$, if it is better to call the second one;
- $3$, if it doesn't matter which elevator to call (both elevators will arrive in the same time).
3
1 2 3
3 1 2
3 2 1
1
3
2
Note
In the first test case of the example, the first elevator is already on the floor of $1$.
In the second test case of the example, when called, the elevators would move as follows:
- At the time of the call, the first elevator is on the floor of $3$, and the second one is on the floor of $1$, but is already going to another floor;
- in $1$ second after the call, the first elevator would be on the floor $2$, the second one would also reach the floor $2$ and now can go to the floor $1$;
- in $2$ seconds, any elevator would reach the floor $1$.
In the third test case of the example, the first elevator will arrive in $2$ seconds, and the second in $1$.
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