long primeXor(vector<int> arr) {
    vector<bool> prime(8192, true);
    prime[0] = false, prime[1] = false;
    for (int p = 2; p*p <= 8191; p++) {
        if (prime[p] == true) {
            for (int i = p*p; i <= 8191; i += p)
                prime[i] = false;
        }
    }
    long total = 0, mod = 1000000007;
    vector<long> counter(8192);
    vector<int> dupe(4501), unique;
    for (int i=0; i < arr.size(); i++) {
        if (dupe[arr[i]] == 0) unique.push_back(arr[i]);
        dupe[arr[i]]++;
    }
    counter[0] = 1;
    for (int i=0; i < unique.size(); i++) {
        vector<long> temporary = counter;
        int F = dupe[unique[i]]/2;
        for (int j=0; j < 8192; j++) {
            int K = unique[i]^j;
            counter[j] = (counter[j] + temporary[j]*F) % mod;
            if (dupe[unique[i]] % 2 == 0) {
                counter[K] = (counter[K] + temporary[j]*F) % mod;
            } else {
                counter[K] = (counter[K] + temporary[j]*(F+1)) % mod;
            }
        }
    }
    for (int i=0; i < counter.size(); i++) {
        if (prime[i]) total = (total + counter[i]) % mod;
    }
    return total;
}