The solution to CCC '17 S3 - Nailed It!, in case anyone is interested, is as follows (confirmed to pass test cases):

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Nailed_It {
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    public static void main(String args[]) throws IOException {
        int n = Integer.parseInt(br.readLine());
        String tokens[] = br.readLine().split(" ");
        int woodlen[] = new int[4001], boardlen[] = new int[4001];
        for(int i = 0; i < n; i++)
            woodlen[Integer.parseInt(tokens[i])]++;
        for(int i = 2; i < 4001; i++) {
            for(int j = 1; j <= i / 2; j++) {
                if(j == i - j)
                    boardlen[i] += woodlen[j] / 2;
                else
                    boardlen[i] += Math.min(woodlen[j], woodlen[i - j]);
            }
        }
        int maxlen = Integer.MIN_VALUE, numways = 0;
        for(int i = 2; i < 4001; i++) {
            if(boardlen[i] > maxlen) {
                maxlen = boardlen[i];
                numways = 1;
            } else if(boardlen[i] == maxlen)
                numways++;
        }
        System.out.print(maxlen + " " + numways);
    }
}