shortening for competitive programming
#define pb push_back
#define pob pop_back
#define all(a) begin(a), end(a)
#define f first
#define s second
#define mp make_pair
#define umap unordered_map
#define uset unordered_set
#define ca const auto&
#define debug(x) cerr << #x << " = " << x << endl
#define all(v) begin(v), end(v)
#define forn(i, n) for(size_t i = 0; i < n; ++i)
#define forsn(i,s,n) for(size_t i = s; i < n; ++i)
#define rforn(i,s) for(size_t i = s; i >= 0; --i)
#define rforsn(i,s,n) for(ll i = s; i >= n; --i)
#define foreach(i, n) for (auto&(i) : (n))
#define cin(type, x) type x; cin>>x;
#define cin2(type, x, y) type x, y; cin>>x>>y;
#define cin3(type, x, y, z) type x, y, z; cin>>x>>y>>z;
#define cin4(type, x, y, z, t) type x, y, z, t; cin>>x>>y>>z>>t;
#define belongs(c, x) (find(begin(c), end(c), x) != end(c))
#define belongs_if(c, x) (find_if(begin(c), end(c), x) != end(c))
#define max3(a,b,c) (max((a),max((b),(c))))
using ull = unsigned long long int;
using ll = long long int;
using uld = unsigned long double;
using ld = long double;
using us = unsigned short;