Problem Statement

kamipeipaa is a science student, so he loves experiments. Today he is conducting an experiment in which he combines two samples, each having some moisture.
kamipeipaa has $2N$ samples. The moisture of the $i$-th sample is represented by an integer $A_i$. He repeats the operation of choosing two of these samples and combining them $N$ times. The moisture of a combined substance is the sum of the moistures of the two samples used to make it. A combined substance is called $Dry$ if its moisture is negative, $Wet$ if it is positive, and $Moist$ if it is zero. Combined substances are dangerous, so they must not be used. Naturally, the samples used in a combination are consumed.

kamipeipaa is about to conduct the experiment, and he wonders how many $Dry$ substances, $Wet$ substances, and $Moist$ substances he can make at most as results of combining. Please tell him.

Input

$N$
$A_1$ $A_2$ $.$ $.$ $.$ $A_{2N}$

The first line contains an integer $N(1 \le N \le 10^{5})$ representing the number of combinations to perform. The second line contains space-separated integers $A_i(-10^{5} \le A_i \le 10^{5})$ representing the moisture of the samples.

Output

Output on one line, separated by spaces, the maximum number of $Dry$ substances, $Wet$ substances, and $Moist$ substances that can be made among the resulting combined substances.

Sample

4
-4 -3 -2 -1 1 2 3 4

3 3 4

2
1 2 3 4

0 2 0