A game is being played which initially consists of $n$ players. On fouls, the referee is allowed to award yellow and red cards. The total number of yellow cards $y$ and red cards $r$ awarded to players is known for the game.

There are $2$ ways a player can be suspended:

• Receiving a red card.
• Receiving $2$ yellow cards.

Once a player is suspended, they are removed from the game and can't receive any more cards. Determine the maximum number of players suspended from the game possible.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 500$). The description of the test cases follows.

The first line of each test case contains an integer $n$ ($1 \le n \le 100$).

The second line of each test case contains two integers $y$ and $r$ ($0 \le r \le n$, $0 \le y + r \le 2n$).

Output

For each test case, print one line containing a single integer — denoting the maximum number of players suspended from the game possible.

Note

For the first test case:

• One of the possible ways to achieve maximum: Player $2$ receives a red card, Player $3$ receives a yellow card followed by a red card.
• This way Player $2$ and $3$ are suspended.

For the second test case:

• No cards are awarded at all, so no one is suspended.

For the third test case:

• One of the possible ways to achieve maximum: Player $1$ receives $2$ yellow cards, Player $2$ receives $2$ yellow cards, and Player $4$ receives $2$ yellow cards.
• This way Player $1$, $2$, and $4$ are suspended.

Samples

5
3
1 2
2
0 0
4
6 0
3
3 3
10
11 5

2
0
3
3
10