#pragma region Macros #pragma GCC optimize("O3") #include #define ll long long #define ld long double #define rep2(i,a,b) for(ll i=a;i<=b;++i) #define rep(i,n) for(ll i=0;i=b;i--) #define pii pair #define pll pair #define pq priority_queue #define pb push_back #define eb emplace_back #define vec vector #define vecll vector #define vecpii vector #define vecpll vector #define vec2(a,b) vector(a,vec(b)) #define vec2ll(a,b) vector(a,vecll(b)) #define vec3(a,b,c) vector>(a,vec2(b,c)) #define vec3ll(a,b,c) vector>(a,vec2ll(b,c)) #define fi first #define se second #define all(c) begin(c),end(c) #define ios ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0); #define lb(c,x) distance(c.begin(),lower_bound(all(c),(x))) #define ub(c,x) distance(c.begin(),upper_bound(all(c),(x))) using namespace std; int in() {int x;cin>>x;return x;} ll lin() {ll x;cin>>x;return x;} string stin() {string s;cin>>s;return s;} template inline bool chmax(T& a,T b){if(a inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} vec iota(int n){vec a(n);iota(all(a),0);return a;} void print(){putchar(' ');} void print(bool a){cout< void print(const vector&); template void print(const array&); template void print(const pair& p); template void print(const T (&)[size]); template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout<<" "; print(*i); } cout< void print(const deque& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout<<" "; print(*i); } } template void print(const array& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout<<" "; print(*i); } } template void print(const pair& p){ cout<<'(';print(p.first); cout<<","; print(p.second);cout<<')'; } template void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ cout<<" "; print(*i); } } template void print(const T& a){ cout << a; } int out(){ putchar('\n'); return 0; } template int out(const T& t){ print(t); putchar('\n'); return 0; } template int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; } ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); } #define _GLIBCXX_DEBU #define endl '\n' #ifdef _MY_DEBUG #undef endl #define debug(x) cout<<#x<<": "< void err(const T& t){ print(t); cout<<" ";} template void err(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); } #else #define debug(x) template void err(const T&...){} #endif #pragma endregion struct UnionFind { vector< int > data; UnionFind(int sz) { data.assign(sz, -1); } bool unite(int x, int y) { x = find(x), y = find(y); if(x == y) return (false); if(data[x] > data[y]) swap(x, y); data[x] += data[y]; data[y] = x; return (true); } int find(int k) { if(data[k] < 0) return (k); return (data[k] = find(data[k])); } int size(int k) { return (-data[find(k)]); } }; signed main(){ ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0);cout<