#include <bits/stdc++.h> using namespace std; using ll = long long; using ld = long double; #define fi first #define se second #define vi vector<int> #define vll vector<long long> #define pii pair<int, int> #define pll pair<long long, long long> #define pb push_back #define mp make_pair #define eb emplace_back #define all(x) (x).begin(), (x).end() #define sz(x) (int)(x).size() mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count()); mt19937_64 rng64(chrono::high_resolution_clock::now().time_since_epoch().count()); inline int rand(int l,int r){return uniform_int_distribution<int>(l, r)(rng);} inline ll rand(ll l,ll r){return uniform_int_distribution<ll>(l, r)(rng64);} #ifdef DEBUG auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";} auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";} #define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X) #else #define debug(...){} #endif struct custom_hash { static uint64_t splitmix64(uint64_t x) { x += 0x9e3779b97f4a7c15; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9; x = (x ^ (x >> 27)) * 0x94d049bb133111eb; return x ^ (x >> 31); } size_t operator()(uint64_t x) const { static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count(); return splitmix64(x + FIXED_RANDOM); } }; const int MAXN = 1e6 + 7; const int MAXK = 30; int A[MAXN]; ll res[MAXK]; int n; void solve(vi vec, int k){ if(k == MAXK){ return; } //debug(vec); //debug(k); //jest posortowany ll mod = (1LL << (k + 1)); ll p2 = (1LL << k); vector<pll> range = {mp(p2, 2 * p2 - 1), mp(3 * p2, 4 * p2 - 1)}; for(int i = 0; i < 2; i++){ int wsk1 = 0; int wsk2 = 0; //debug(range[i]); //for(auto ele : vec){ // cerr << (A[ele] % mod) << ' '; // } //cerr << '\n'; for(int j = 0; j < n; j++){ ll curr = A[vec[j]] % mod; while(wsk2 + 1 <= j && curr + (A[vec[wsk2 + 1]] % mod) <= range[i].se){ wsk2++; } while(wsk1 < wsk2 && curr + (A[vec[wsk1]] % mod) < range[i].fi){ wsk1++; } // cerr << j << ' ' << curr << ' ' << wsk1 << ' ' << wsk2 << '\n'; if(curr + (A[vec[wsk1]] % mod) >= range[i].fi && curr + (A[vec[wsk1]] % mod) <= range[i].se){ // cerr << "ADD: " << k << ' ' << wsk2 - wsk1 + 1 << '\n'; res[k] = (ll)res[k] + wsk2 - wsk1 + 1; } } } //posortuj vi vec0, vec1; for(auto ele : vec){ if(A[ele] & mod){ vec1.pb(ele); }else{ vec0.pb(ele); } } vec0.insert(vec0.end(), all(vec1)); solve(vec0, k + 1); } int main(){ ios_base::sync_with_stdio(0); cin.tie(NULL); cout.tie(NULL); cin >> n; vi pos0, pos1; for(int i = 1; i <= n; i++){ cin >> A[i]; if(A[i] & 1){ pos1.pb(i); }else{ pos0.pb(i); } } pos0.insert(pos0.end(), all(pos1)); solve(pos0, 0); ll ksor = 0LL; for(int i = 0; i < MAXK; i++){ if(res[i] & 1){ ksor = (ll)ksor + (1LL << i); } } cout << ksor << '\n'; return 0; }