Raðir

You really like playing card games with your friend. He recently introduced you to a new card game. Initially $p$ cards are dealt to both players. You then take turns drawing a card to your hand and then discarding a card from your hand. The goal is to obtain a sequence in your hand. A sequence is any three cards of the same suit such that if the card of the smallest value has value $a$ then the other two cards have value $a + 1$ and $a + 2$. You can declare victory at the end of your turn, as long as you have a sequence in your hand.

You just lost a game to your friend. This doesn’t bother you too much, since you just learned how to play the game, but you want to learn from your mistakes. Looking over your cards you wonder how early you could have achieved a sequence had you played optimally.

Input

The first line of the input contains two integers: $n$, the total number of cards, and $p$, the number of cards you can keep in your hand, with $3 \leq p \leq n \leq 10^6$. Then there are $n$ lines, the $j$-th containing an integer $1 \leq c_ j \leq 4$ and an integer $1 \leq k_ j \leq 13$, the color and suit of the $j$-th card you receive. The first $p$ cards are the cards you got dealt initially, and the subsequent $n - p$ cards are the cards you drew.

Output

The output should contain one integer, the fewest number of turns it could have taken you to obtain a sequence. If no sequence can be obtained output “neibb”.

Sample Input 1 Sample Output 1
5 3
1 1
1 2
4 3
2 3
1 3
2
Sample Input 2 Sample Output 2
5 3
1 1
1 2
1 4
1 3
1 5
1
Sample Input 3 Sample Output 3
3 3
3 2
3 3
3 1
1
Sample Input 4 Sample Output 4
5 3
1 1
1 2
1 4
1 5
1 7
neibb