class mf_graph: """It solves maximum flow problem. """ def __init__(self, n): """It creates a graph of n vertices and 0 edges. Constraints ----------- > 0 <= n <= 10 ** 8 Complexity ---------- > O(n) """ self.n = n self.g = [[] for _ in range(self.n)] self.pos = [] def add_edge(self, from_, to, cap): """It adds an edge oriented from the vertex `from_` to the vertex `to` with the capacity `cap` and the flow amount 0. It returns an integer k such that this is the k-th edge that is added. Constraints ----------- > 0 <= from_, to < n > 0 <= cap Complexity ---------- > O(1) amortized """ # assert 0 <= from_ < self.n # assert 0 <= to < self.n # assert 0 <= cap m = len(self.pos) self.pos.append((from_, len(self.g[from_]))) self.g[from_].append(self.__class__._edge(to, len(self.g[to]), cap)) self.g[to].append(self.__class__._edge(from_, len(self.g[from_]) - 1, 0)) return m class edge: def __init__(self, from_, to, cap, flow): self.from_ = from_ self.to = to self.cap = cap self.flow = flow def get_edge(self, i): """It returns the current internal state of the edges. The edges are ordered in the same order as added by add_edge. Complexity ---------- > O(1) """ # assert 0 <= i < len(self.pos) _e = self.g[self.pos[i][0]][self.pos[i][1]] _re = self.g[_e.to][_e.rev] return self.__class__.edge(self.pos[i][0], _e.to, _e.cap + _re.cap, _re.cap) def edges(self): """It returns the current internal state of the edges. The edges are ordered in the same order as added by add_edge. Complexity ---------- > O(m), where m is the number of added edges. """ result = [] for i in range(len(self.pos)): _e = self.g[self.pos[i][0]][self.pos[i][1]] _re = self.g[_e.to][_e.rev] result.append(self.__class__.edge(self.pos[i][0], _e.to, _e.cap + _re.cap, _re.cap)) return result def change_edge(self, i, new_cap, new_flow): """It changes the capacity and the flow amount of the ii-th edge to new_cap and new_flow, respectively. It doesn't change the capacity or the flow amount of other edges. See Appendix for further details. Constraints ----------- > 0 <= newflow <= newcap Complexity ---------- > O(1) """ # assert 0 <= i < len(self.pos) # assert 0 <= new_flow <= new_cap _e = self.g[self.pos[i][0]][self.pos[i][1]] _re = self.g[_e.to][_e.rev] _e.cap = new_cap - new_flow _re.cap = new_flow def _bfs(self, s, t): self.level = [-1] * self.n self.level[s] = 0 q = [s] while q: nq = [] for v in q: for e in self.g[v]: if e.cap and self.level[e.to] == -1: self.level[e.to] = self.level[v] + 1 if e.to == t: return True nq.append(e.to) q = nq return False def _dfs(self, s, t, up): st = [t] while st: v = st[-1] if v == s: st.pop() flow = up for w in st: e = self.g[w][self.it[w]] flow = min(flow, self.g[e.to][e.rev].cap) for w in st: e = self.g[w][self.it[w]] e.cap += flow self.g[e.to][e.rev].cap -= flow return flow while self.it[v] < len(self.g[v]): e = self.g[v][self.it[v]] w = e.to cap = self.g[e.to][e.rev].cap if cap and self.level[v] > self.level[w]: st.append(w) break self.it[v] += 1 else: st.pop() self.level[v] = self.n return 0 def flow(self, s, t, flow_limit=float('inf')): """It augments the flow from s to t as much as possible. It returns the amount of the flow augmented. You may call it multiple times. See Appendix in the document of AC Library for further details. Constraints ----------- > s != t Complexity ---------- > O(min(n^(2/3)m, m^(3/2))) (if all the capacities are 1) or > O(n^2 m) (general), where m is the number of added edges. """ # assert 0 <= s < self.n # assert 0 <= t < self.n # assert s != t flow = 0 while flow < flow_limit and self._bfs(s, t): self.it = [0] * self.n while flow < flow_limit: f = self._dfs(s, t, flow_limit - flow) if not f: break flow += f return flow def min_cut(self, s): """It returns a vector of length n, such that the i-th element is true if and only if there is a directed path from s to i in the residual network. The returned vector corresponds to a s−t minimum cut after calling flow(s, t) exactly once without flow_limit. See Appendix in the document of AC Library for further details. Complexity ---------- > O(n + m), where m is the number of added edges. """ visited = [False] * self.n q = [s] while q: nq = [] for p in q: visited[p] = True for e in self.g[p]: if e.cap and not visited[e.to]: nq.append(e.to) q = nq return visited class _edge: def __init__(self, to, rev, cap): self.to = to self.rev = rev self.cap = cap def popcount(m): return bin(m).count('1') n=int(input()) a=list(map(int,input().split())) s,t=n,n+1 g=mf_graph(n+2) inf=min(n,10) for i in range(n): if popcount(a[i])%2==0: g.add_edge(s,i,1) else: g.add_edge(i,t,1) for i in range(n): for j in range(i+1,n): if popcount(a[i]^a[j])==1: if popcount(a[i])%2==0: g.add_edge(i,j,inf) else: g.add_edge(j,i,inf) print(n-g.flow(s,t))