#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; typedef long long ll; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--) #define repk(i, k, n) for (int i = k; i < (int)(n); i++) #define all(v) v.begin(), v.end() #define mod1 1000000007 #define mod2 998244353 #define mod3 100000007 #define vi vector #define vs vector #define vc vector #define vl vector #define vb vector #define vvi vector> #define vvc vector> #define vvl vector> #define vvb vector> #define vvvi vector>> #define vvvl vector>> #define pii pair #define pil pair #define pli pair #define pll pair #define vpii vector> #define vpll vector> #define vvpii vector>> #define vvpll vector>> template void debug(T e) { cerr << e << endl; } template void debug(vector &v) { rep(i, v.size()) { cerr << v[i] << " "; } cerr << endl; } template void debug(vector> &v) { rep(i, v.size()) { rep(j, v[i].size()) { cerr << v[i][j] << " "; } cerr << endl; } } template void debug(vector> &v) { rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; } } template void debug(set &st) { for (auto itr = st.begin(); itr != st.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(multiset &ms) { for (auto itr = ms.begin(); itr != ms.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(map &mp) { for (auto itr = mp.begin(); itr != mp.end(); itr++) { cerr << itr->first << " " << itr->second << endl; } } void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << H << " "; debug_out(T...); } using mint = modint998244353; void debug_mint1(vector &vec) { for (int i = 0; i < vec.size(); i++) { cerr << vec[i].val() << " "; } cerr << endl; } void debug_mint2(vector> &vec) { for (int i = 0; i < vec.size(); i++) { for (int j = 0; j < vec[i].size(); j++) { cerr << vec[i][j].val() << " "; } cerr << endl; } } ll my_pow(ll x, ll n, ll mod) { //  繰り返し二乗法.x^nをmodで割った余り. ll ret; if (n == 0) { ret = 1; } else if (n % 2 == 1) { ret = (x * my_pow((x * x) % mod, n / 2, mod)) % mod; } else { ret = my_pow((x * x) % mod, n / 2, mod); } return ret; } ll inv(ll x, ll mod) { return my_pow(x, mod - 2, mod); } vector fwht(vector &vec, ll K){ ll h = 1; vector vec_cpy(vec.size()); for (ll i = 0; i < vec.size(); i++){ vec_cpy[i] = vec[i]; } for (ll k = 0; k < K; k++){ for (ll i = 0; i < vec.size(); i += h * 2){ for (ll j = i; j < i + h; j++){ ll v1 = vec_cpy[j]; ll v2 = vec_cpy[j + h]; vec_cpy[j] = (v1 + v2) % mod2; vec_cpy[j + h] = (v1 + mod2 - v2) % mod2; } } h *= 2; } return vec_cpy; } vector xor_convolution(vector &a, vector &b, ll K){ vector a_cpy = fwht(a, K); vector b_cpy = fwht(b, K); vector c(a.size()); for (ll i = 0; i < a.size(); i++){ c[i] = (a_cpy[i] * b_cpy[i]) % mod2; } vector c_cpy = fwht(c, K); for (ll i = 0; i < c.size(); i++){ c_cpy[i] = (c_cpy[i] * inv(1 << K, mod2)) % mod2; } return c_cpy; } int main() { ll N; cin >> N; vector A(N); rep(i, N) cin >> A[i]; // この部分の計算量削減 mint a2 = 0; /*for (ll i = 0; i < N; i++){ for (ll j = 0; j < N; j++){ for (ll k = 0; k < N; k++){ a2 -= mint(8) * min((A[i] ^ A[j]), (A[i] ^ A[k])); } } }*/ mint ans = 0; ll L = (1 << 18); ll B = 18; vector>>> vals(B, vector>>(2, vector>(B, vector(2, 0)))); for (ll i = 0; i < N; i++){ for (ll j = 0; j < B; j++){ for (ll k = 0; k < B; k++){ vals[j][(A[i] >> j) & 1][k][(A[i] >> k) & 1]++; } } } vector>> trie(2 * L, vector>(B, vector(2, 0))); for (ll i = 0; i < N; i++){ for (ll j = 0; j < B; j++){ trie[A[i] + L][j][(A[i] >> j) & 1]++; } } for (ll j = 0; j < B; j++){ for (ll k = 0; k < 2; k++){ for (ll i = L - 1; i >= 1; i--){ trie[i][j][k] += trie[2 * i][j][k]; trie[i][j][k] += trie[2 * i + 1][j][k]; } } } // この情報から和を求められる for (ll i = 1; i < L; i++){ ll msb = -1; for (ll j = 0; j < B; j++){ if ((i >> j) & 1) msb = j; } msb = B - 1 - msb; for (ll j = 0; j < B; j++){ mint pj = mint(1LL << j); mint s0 = mint(trie[i * 2][j][0] + trie[i * 2][j][1]); mint s1 = mint(trie[i * 2 + 1][j][0] + trie[i * 2 + 1][j][1]); a2 += mint(2) * s0 * mint(vals[msb][1][j][0]) * mint(trie[2 * i + 1][j][1]) * pj; a2 += mint(2) * s0 * mint(vals[msb][1][j][1]) * mint(trie[2 * i + 1][j][0]) * pj; a2 += mint(2) * s1 * mint(vals[msb][0][j][0]) * mint(trie[2 * i][j][1]) * pj; a2 += mint(2) * s1 * mint(vals[msb][0][j][1]) * mint(trie[2 * i][j][0]) * pj; } } vector coef(L, 0); rep(i, N) coef[A[i]]++; vector coef2(L, 0); rep(i, L){ coef2[i] = (coef[i] * coef[i]) % mod2; } vector> val2(B, vector(2, 0)); for (ll i = 0; i < L; i++){ for (ll j = 0; j < B; j++){ val2[j][(i >> j) & 1] += coef2[i]; val2[j][(i >> j) & 1] %= mod2; } } for (ll i = 0; i < N; i++){ for (ll j = 0; j < B; j++){ mint pj = mint(1LL << j); a2 += pj * mint(val2[j][1 - ((A[i] >> j) & 1)]); } } a2 *= mint(mod2 - 8); vector conv = xor_convolution(coef, coef, B); conv[0] -= N; mint now_sum = 0; mint now_cnt = 0; for (ll i = 0; i < L; i++){ ans += mint(conv[i]) * (mint(i) * now_cnt - now_sum); now_sum += i * conv[i]; now_cnt += conv[i]; } for (ll i = 0; i < L; i++){ ans += (4 * conv[i] * i); } a2 += N * 8 * now_sum; cout << (ans * mint(2) - a2).val() << endl; }