class Euler39 {

    private static class Options {
        int limit = 1000;
        boolean runCheckpoints = true;
    }

    private static boolean parseIntAfterPrefix(String arg, String prefix, Options options) {
        if (!arg.startsWith(prefix)) {
            return false;
        }
        String tail = arg.substring(prefix.length());
        if (tail.isEmpty()) {
            return false;
        }

        int parsed = 0;
        for (int i = 0; i < tail.length(); i++) {
            char c = tail.charAt(i);
            if (c < '0' || c > '9') {
                return false;
            }
            parsed = parsed * 10 + (c - '0');
        }
        options.limit = parsed;
        return true;
    }

    private static boolean parseArguments(String[] args, Options options) {
        for (String arg : args) {
            if (arg.equals("--skip-checkpoints")) {
                options.runCheckpoints = false;
                continue;
            }
            if (parseIntAfterPrefix(arg, "--limit=", options)) {
                continue;
            }
            System.err.println("Unknown argument: " + arg);
            return false;
        }
        return options.limit >= 12;
    }

    private static int solve(int limit) {
        int[] solutions = new int[limit + 1];

        for (int a = 1; a <= limit / 3; a++) {
            for (int b = a; b <= (limit - a) / 2; b++) {
                int c2 = a * a + b * b;
                int c = (int) Math.sqrt(c2);
                if (c * c != c2) {
                    continue;
                }
                int p = a + b + c;
                if (p <= limit) {
                    solutions[p]++;
                }
            }
        }

        int bestP = 0;
        int bestCount = -1;
        for (int p = 0; p <= limit; p++) {
            if (solutions[p] > bestCount) {
                bestCount = solutions[p];
                bestP = p;
            }
        }

        return bestP;
    }

    private static boolean runCheckpoints() {
        if (solve(120) != 120) {
            System.err.println("Checkpoint failed for limit=120");
            return false;
        }
        return true;
    }

    public static void main(String[] args) {
        Options options = new Options();
        if (!parseArguments(args, options)) {
            System.exit(1);
        }
        if (options.runCheckpoints && !runCheckpoints()) {
            System.exit(2);
        }

        System.out.println(solve(options.limit));
    }
}