import java.util.ArrayList;

class Solution {
    private static final double eps = 0.000001;

    public boolean judgePoint24(int[] nums) {
        ArrayList<Double> list = new ArrayList<>();
        for (int n : nums) list.add((double) n);
        return dfs(list);
    }

    private boolean dfs(ArrayList<Double> list) {
        if (list.size() == 1 && Math.abs(list.get(0) - 24.0) < eps) return true;
        for (int i = 0; i < list.size() - 1; i++) {
            for (int j = i + 1; j < list.size(); j++) {
                ArrayList<Double> candidate = new ArrayList<>();
                double n1 = list.get(i), n2 = list.get(j);
                candidate.add(n1 + n2);
                candidate.add(n1 - n2);
                candidate.add(n2 - n1);
                candidate.add(n1 * n2);
                if (n2 != 0.0) candidate.add(n1 / n2);
                if (n1 != 0.0) candidate.add(n2 / n1);
                ArrayList<Double> next = new ArrayList<>();
                for (int k = 0; k < list.size(); k++)
                    if (k != i && k != j)
                        next.add(list.get(k));
                for (int k = 0; k < candidate.size(); k++) {
                    next.add(candidate.get(k));
                    if (dfs(next)) return true;
                    next.remove(next.size() - 1);
                }
            }
        }
        return false;
    }
}