Rock-paper-scissors is a common game: rock beats scissors, scissors beats paper, and paper beats rock. If both players choose the same gesture, it is a draw. In the 8th episode of the second season of The Big Bang Theory, an upgraded version of rock-paper-scissors was introduced. This version adds two new gestures to the traditional game:

• Spock: One of the protagonists of Star Trek.
• Lizard: An antagonist from Star Trek.

The win-loss relationships for these five gestures are shown in Table 1, which lists the results for Player A vs. Player B.

Now, Player A and Player B are playing this upgraded version. It is known that their gestures follow a periodic pattern, though the cycle lengths are not necessarily equal. For example: if Player A plays with a cycle of length $6$ ("Rock-Paper-Rock-Scissors-Lizard-Spock"), their sequence of gestures is "Rock-Paper-Rock-Scissors-Lizard-Spock-Rock-Paper-Rock-Scissors-Lizard-Spock-...". If Player B plays with a cycle of length $5$ ("Scissors-Rock-Paper-Spock-Lizard"), their sequence of gestures is "Scissors-Rock-Paper-Spock-Lizard-Scissors-Rock-Paper-Spock-Lizard-...".

Given that Player A and Player B play $N$ rounds in total, the winner of each round gets $1$ point, and the loser gets $0$ points. In the event of a draw, both players get $0$ points. Please calculate the final scores of both players after $N$ rounds.

Input

The first line contains three integers: $N, N_A, N_B$, representing the total number of rounds, the cycle length of Player A, and the cycle length of Player B, respectively. The numbers are separated by a space.

The second line contains $N_A$ integers representing the pattern of Player A, and the third line contains $N_B$ integers representing the pattern of Player B. Here, 0 represents "Scissors", 1 represents "Rock", 2 represents "Paper", 3 represents "Lizard", and 4 represents "Spock". The numbers are separated by a space.

Output

Output a single line containing two integers separated by a space, representing the scores of Player A and Player B, respectively.

Examples

Input 1

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

Output 1

6 2

Input 2

9 5 5
0 1 2 3 4
1 0 3 2 4

Output 2

4 4

Constraints

For $100\%$ of the data, $0 < N \leq 200, 0 < N_A \leq 200, 0 < N_B \leq 200$.