#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#include <bits/extc++.h>
using namespace std;
/*
#include <atcoder/all>
using namespace atcoder;
*/
/*
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using bll = boost::multiprecision::cpp_int;
using bdouble = boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100>>;
using namespace boost::multiprecision;
*/
#if defined(LOCAL_TEST) || defined(LOCAL_DEV)
	#define BOOST_STACKTRACE_USE_ADDR2LINE
	#define BOOST_STACKTRACE_ADDR2LINE_LOCATION /usr/local/opt/binutils/bin/addr2line
	#define _GNU_SOURCE 1
	#include <boost/stacktrace.hpp>
#endif
#ifdef LOCAL_TEST
	namespace std {
		template <typename T> class dvector : public std::vector<T> {
		public:
			using std::vector<T>::vector;
			template <typename T_ = T, typename std::enable_if_t<std::is_same_v<T_, bool>, std::nullptr_t> = nullptr>
			std::vector<bool>::reference operator[](std::size_t n) {
				if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n);
			}
			template <typename T_ = T, typename std::enable_if_t<std::is_same_v<T_, bool>, std::nullptr_t> = nullptr>
			const T_ operator[](std::size_t n) const {
				if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n);
			}
			template <typename T_ = T, typename std::enable_if_t<!std::is_same_v<T_, bool>, std::nullptr_t> = nullptr>
			T_& operator[](std::size_t n) {
				if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n);
			}
			template <typename T_ = T, typename std::enable_if_t<!std::is_same_v<T_, bool>, std::nullptr_t> = nullptr>
			const T_& operator[](std::size_t n) const {
				if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n);
			}
		};
		template <typename T, typename Compare = std::less<T>, typename Allocator = std::allocator<T>> class dmultiset : public std::multiset<T,Compare,Allocator> {
		public:
			using std::multiset<T,Compare,Allocator>::multiset;
			const typename std::multiset<T,Compare,Allocator>::iterator erase(const typename std::multiset<T,Compare,Allocator>::iterator it) {
				return std::multiset<T,Compare,Allocator>::erase(it);
			}
			std::size_t erase([[maybe_unused]] const T& x) {
				std::cerr << boost::stacktrace::stacktrace() << '\n'; assert(false);
			}
			std::size_t erase_all_elements(const T& x) {
				return std::multiset<T,Compare,Allocator>::erase(x);
			}
		};
	}
	#define vector dvector
	#define multiset dmultiset
	class SIGFPE_exception : std::exception {};
	class SIGSEGV_exception : std::exception {};
	void catch_SIGFPE([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGFPE_exception(); }
	void catch_SIGSEGV([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGSEGV_exception(); }
	signed convertedmain();
	signed main() { signal(SIGFPE, catch_SIGFPE); signal(SIGSEGV, catch_SIGSEGV); return convertedmain(); }
	#define main() convertedmain()
#else
	#define erase_all_elements erase
#endif
#ifdef LOCAL_DEV
	template <typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::pair<T1, T2>& p) {
		return s << "(" << p.first << ", " << p.second << ")"; }
	template <typename T, std::size_t N> std::ostream& operator<<(std::ostream& s, const std::array<T, N>& a) {
		s << "{ "; for (std::size_t i = 0; i < N; ++i){ s << a[i] << "\t"; } s << "}"; return s; }
	template <typename T, typename Compare> std::ostream& operator<<(std::ostream& s, const std::set<T, Compare>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template <typename T, typename Compare> std::ostream& operator<<(std::ostream& s, const std::multiset<T, Compare>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template <typename T1, typename T2, typename Compare> std::ostream& operator<<(std::ostream& s, const std::map<T1, T2, Compare>& m) {
		s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; }
	template <typename T> std::ostream& operator<<(std::ostream& s, const std::deque<T>& v) {
		for (std::size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; }
	template <typename T> std::ostream& operator<<(std::ostream& s, const std::vector<T>& v) {
		for (std::size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; }
	template <typename T> std::ostream& operator<<(std::ostream& s, const std::vector<std::vector<T>>& vv) {
		s << "\\\n"; for (std::size_t i = 0; i < vv.size(); ++i){ s << vv[i] << "\n"; } return s; }
	template <typename T, std::size_t N, typename std::enable_if_t<!std::is_same_v<T, char>, std::nullptr_t> = nullptr> std::ostream& operator<<(std::ostream& s, const T (&v)[N]) {
		for (std::size_t i = 0; i < N; ++i){ s << v[i]; if (i < N - 1) s << "\t"; } return s; }
	template <typename T, std::size_t N, std::size_t M, typename std::enable_if_t<!std::is_same_v<T, char>, std::nullptr_t> = nullptr> std::ostream& operator<<(std::ostream& s, const T (&vv)[N][M]) {
		s << "\\\n"; for (std::size_t i = 0; i < N; ++i){ s << vv[i] << "\n"; } return s; }
	#if __has_include(<ext/pb_ds/assoc_container.hpp>)
		template <typename Key, typename Compare> std::ostream& operator<<(std::ostream& s, const __gnu_pbds::tree<Key, __gnu_pbds::null_type, Compare, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>& se) {
			s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
		template <typename Key, typename T, typename Hash> std::ostream& operator<<(std::ostream& s, const __gnu_pbds::gp_hash_table<Key, T, Hash>& m) {
			s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; }
	#endif
	void debug_impl() { std::cerr << '\n'; }
	template <typename Head, typename... Tail> void debug_impl(const Head& head, const Tail&... tail) { std::cerr << " " << head << (sizeof...(tail) ? "," : ""); debug_impl(tail...); }
	#define debug(...) do { std::cerr << ":" << __LINE__ << " (" << #__VA_ARGS__ << ") ="; debug_impl(__VA_ARGS__); } while (false)
	constexpr inline long long prodlocal([[maybe_unused]] long long prod, [[maybe_unused]] long long local) { return local; }
#else
	#define debug(...) do {} while (false)
	constexpr inline long long prodlocal([[maybe_unused]] long long prod, [[maybe_unused]] long long local) { return prod; }
#endif
//#define int long long
using ll = long long;
//INT_MAX = (1<<31)-1 = 2147483647, INT64_MAX = (1LL<<63)-1 = 9223372036854775807
constexpr ll INF = std::numeric_limits<ll>::max() == INT_MAX ? (ll)1e9 + 7 : (ll)1e18;
constexpr ll MOD = (ll)1e9 + 7; //primitive root = 5
//constexpr ll MOD = 998244353; //primitive root = 3
constexpr double EPS = 1e-9;
constexpr ll dx[4] = {1, 0, -1, 0};
constexpr ll dy[4] = {0, 1, 0, -1};
constexpr ll dx8[8] = {1, 0, -1, 0, 1, 1, -1, -1};
constexpr ll dy8[8] = {0, 1, 0, -1, 1, -1, 1, -1};
#define repoverload3(_1, _2, _3, name, ...) name
#define rep3(i, a, b) for(ll i=(a), i##_length=(b); i<i##_length; ++i)
#define rep2(i, n) rep3(i, 0, n)
#define rep1(n) rep3(i, 0, n)
#define rep(...) repoverload3(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repeq3(i, a, b) rep3(i, (a)+1, (b)+1)
#define repeq2(i, n) rep3(i, 1, (n)+1)
#define repeq1(n) rep3(i, 1, (n)+1)
#define repeq(...) repoverload3(__VA_ARGS__, repeq3, repeq2, repeq1)(__VA_ARGS__)
#define rrep3(i, a, b) for(ll i=(b)-1; i>=(a); --i)
#define rrep2(i, n) rrep3(i, 0, n)
#define rrep1(n) rrep3(i, 0, n)
#define rrep(...) repoverload3(__VA_ARGS__, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define rrepeq3(i, a, b) rrep3(i, (a)+1, (b)+1)
#define rrepeq2(i, n) rrep3(i, 1, (n)+1)
#define rrepeq1(n) rrep3(i, 1, (n)+1)
#define rrepeq(...) repoverload3(__VA_ARGS__, rrepeq3, rrepeq2, rrepeq1)(__VA_ARGS__)
#define all(v) std::begin(v), std::end(v)
#define rall(v) std::rbegin(v), std::rend(v)
void p() { std::cout << '\n'; }
template <typename Head, typename... Tail> void p(const Head& head, const Tail&... tail) { std::cout << head << (sizeof...(tail) ? " " : ""); p(tail...); }
template <typename T> inline void pv(const std::vector<T>& v) { for(ll i=0, N=v.size(); i<N; i++) std::cout << v[i] << " \n"[i==N-1]; }
template <typename T> inline bool chmax(T& a, T b) { return a < b && (a = b, true); }
template <typename T> inline bool chmin(T& a, T b) { return a > b && (a = b, true); }
template <typename T> inline void uniq(std::vector<T>& v) { std::sort(v.begin(), v.end()); v.erase(std::unique(v.begin(), v.end()), v.end()); }
template <typename T> inline ll sz(const T& v) { return std::size(v); }
template <typename T, std::size_t N> std::vector<T> make_vector_impl(std::vector<ll>& sizes, typename std::enable_if<(N==1), const T&>::type x) { return std::vector<T>(sizes.front(),x); }
template <typename T, std::size_t N> auto make_vector_impl(std::vector<ll>& sizes, typename std::enable_if<(N>1), const T&>::type x) { ll size=sizes.back(); sizes.pop_back(); return std::vector<decltype(make_vector_impl<T,N-1>(sizes,x))>(size,make_vector_impl<T,N-1>(sizes,x)); }
template <typename T, std::size_t N> auto make_vector(const ll (&sizes)[N], const T& x=T()) { std::vector<ll> s(N); for(std::size_t i=0; i<N; ++i)s[i]=sizes[N-1-i]; return make_vector_impl<T,N>(s,x); }
#if __has_include(<ext/pb_ds/assoc_container.hpp>)
	template <typename Key, typename Mapped, typename Hash = std::hash<Key>, typename std::enable_if_t<std::is_integral_v<Key>, std::nullptr_t> = nullptr> class fmap : public __gnu_pbds::gp_hash_table<Key, Mapped, Hash> {
	public:
		using __gnu_pbds::gp_hash_table<Key, Mapped, Hash>::gp_hash_table;
		template <typename T> fmap(std::initializer_list<std::initializer_list<T>> il) : __gnu_pbds::gp_hash_table<Key, Mapped, Hash>() {
			for (auto&& x : il) __gnu_pbds::gp_hash_table<Key, Mapped, Hash>::insert(std::pair<Key, Mapped>(*x.begin(), *(x.begin() + 1)));
		}
		template <typename T> ll count(const T& x) const {
			return __gnu_pbds::gp_hash_table<Key, Mapped, Hash>::find(x) != __gnu_pbds::gp_hash_table<Key, Mapped, Hash>::end();
		}
	};
#else
	template <typename Key, typename Mapped> using fmap = std::map<Key, Mapped>;
#endif
template <typename T> class each_hepler {
public:
	class iterator {
	public:
		ll _pos;
		typename T::iterator _it;
		iterator(typename T::iterator it): _pos(0), _it(it) {}
		std::pair<ll, typename std::iterator_traits<typename T::iterator>::reference> operator*() const { return {_pos, *_it}; }
		iterator& operator++() { ++_pos; ++_it; return *this; }
		iterator operator++(int) { iterator tmp(*this); ++*this; return tmp; }
		bool operator==(iterator const& it) const { return _it == it._it; }
		bool operator!=(iterator const& it) const { return !(*this == it); }
	};
	T& _container;
	each_hepler(T& t): _container(t) {}
	iterator begin() const { return iterator(_container.begin()); }
	iterator end() const { return iterator(_container.end()); }
};
template <typename T> each_hepler<T> each(T& t) { return each_hepler<T>(t); } // for (auto&& [i, val] : each(v))
template <typename... T> class zip_helper {
public:
	class iterator : std::iterator<std::forward_iterator_tag, std::tuple<decltype(*std::declval<T>().begin())...>> {
	private:
		std::tuple<decltype(std::declval<T>().begin())...> iters_;
		template <std::size_t... I> auto deref(std::index_sequence<I...>) const { return typename iterator::value_type{*std::get<I>(iters_)...}; }
		template <std::size_t... I> void increment(std::index_sequence<I...>) { [[maybe_unused]] auto l = {(++std::get<I>(iters_), 0)...}; }
	public:
		explicit iterator(decltype(iters_) iters) : iters_{std::move(iters)} {}
		iterator& operator++() { increment(std::index_sequence_for<T...>{}); return *this; }
		iterator operator++(int) { auto saved{*this}; increment(std::index_sequence_for<T...>{}); return saved; }
		bool operator!=(const iterator& other) const { return iters_ != other.iters_; }
		auto operator*() const { return deref(std::index_sequence_for<T...>{}); }
	};
	zip_helper(T&... seqs) : begin_{std::make_tuple(seqs.begin()...)}, end_{std::make_tuple(seqs.end()...)} {}
	iterator begin() const { return begin_; }
	iterator end() const { return end_; }
private:
	iterator begin_, end_;
};
template <typename... T> auto zip(T&&... seqs) { return zip_helper<T...>{seqs...}; } // for (auto&& [a, b, c] : zip(A, B, C))

/*-----8<-----template-----8<-----*/

//[lib]segmenttree.cpp
/*
実装では木を 1-indexed の配列で表現している。
ノード k について, 親ノードは k/2, 子ノードは 2k, 2k+1 である。

SegmentTree(n, f, M1):= サイズ n の初期化。
	f は2つの区間の要素をマージする二項演算,
	M1 はモノイドの単位元である。
set(k,x):= k 番目の要素に x を代入する。
build():= セグメント木を構築する。
query(a,b):= 区間 [a,b) に対して二項演算した結果を返す。
update(k,x):= k 番目の要素を x に変更する。
nth_min(x):= 値が0でない要素のうち、小さいものから x 番目のindexを返す。
operator[k] := k 番目の要素を返す。
find_first(a, check) := [a,x) が check を満たす最初の要素位置 x を返す。見つからない場合は -1 を返す。
find_last(b, check) := [x,b) が check を満たす最後の要素位置 x を返す。見つからない場合は -1 を返す。
*/
template< typename Monoid, typename F >
class SegmentTree {
public:
	ll sz;
	vector< Monoid > seg;
	const F f;
	const Monoid M1;

	SegmentTree(ll n, const F &f, const Monoid &M1) : f(f), M1(M1) {
		sz = 1;
		while(sz < n) sz <<= 1;
		seg.assign(2 * sz, M1);
	}

	void set(ll k, const Monoid &x) {
		seg[k + sz] = x;
	}

	void build() {
		for(ll k = sz - 1; k > 0; k--) {
			seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
		}
	}

	void update(ll k, const Monoid &x) {
		k += sz;
		seg[k] = x;
		while(k >>= 1) {
			seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
		}
	}

	Monoid query(ll a, ll b) {
		Monoid L = M1, R = M1;
		for(a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
			if(a & 1) L = f(L, seg[a++]);
			if(b & 1) R = f(seg[--b], R);
		}
		return f(L, R);
	}

	Monoid all_prod() {
		return seg[1];
	}

	Monoid operator[](const ll &k) const {
		return seg[k + sz];
	}

	template< typename C >
	ll find_subtree(ll a, const C &check, Monoid &M, bool type) {
		while(a < sz) {
			Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
			if(check(nxt)) a = 2 * a + type;
			else M = nxt, a = 2 * a + 1 - type;
		}
		return a - sz;
	}

	template< typename C >
	ll find_first(ll a, const C &check) {
		Monoid L = M1;
		if(a <= 0) {
			if(check(f(L, seg[1]))) return find_subtree(1, check, L, false);
			return -1;
		}
		ll b = sz;
		for(a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
			if(a & 1) {
				Monoid nxt = f(L, seg[a]);
				if(check(nxt)) return find_subtree(a, check, L, false);
				L = nxt;
				++a;
			}
		}
		return -1;
	}

	template< typename C >
	ll find_last(ll b, const C &check) {
		Monoid R = M1;
		if(b >= sz) {
			if(check(f(seg[1], R))) return find_subtree(1, check, R, true);
			return -1;
		}
		ll a = sz;
		for(b += sz; a < b; a >>= 1, b >>= 1) {
			if(b & 1) {
				Monoid nxt = f(seg[--b], R);
				if(check(nxt)) return find_subtree(b, check, R, true);
				R = nxt;
			}
		}
		return -1;
	}

	// [L, R)の範囲で関数check を満たす/満たさない境目のindexを返す
	// auto check = [](Monoid data){ 何かしら };
	// 返却値 = 満たさない最初のindex, 返却値-L = 満たす要素数
	// L が固定, たぶん R が機能していない
	template<typename Func>
	ll partitionpoint(ll L, ll R, const Func &check){
		ll x = find_first(L, [&](const Monoid &data){return !check(data);});
		return x==-1||x>R ? R : x;
	}
	// R が固定, たぶん L が機能していない
	// 返却値 = 満たさない最初のindex, R-返却値 = 満たさない要素数
	template<typename Func>
	ll partitionpoint_rev(ll L, ll R, const Func &check){
		ll x = find_last(R, [&](const Monoid &data){return check(data);});
		return x==-1||x<L ? L : x+1;
	}
};
template< typename Monoid, typename F >
std::ostream& operator<<(std::ostream& s, SegmentTree<Monoid,F> seg) { 
	for(ll i=0; i<seg.sz; i++) s << seg[i] << "\t\n"[i==seg.sz-1];
	return s;
}

//[lib]2Dcomp(1点add矩形sum).cpp
//[depends on]segmenttree.cpp
template< typename structure_t, typename get_t, typename update_t, typename merge_f, typename range_get_f, typename update_f>
class SegmentTree2DCompressed {
public:
	//using merge_f = function< get_t(get_t, get_t) >;
	//using range_get_f = function< get_t(structure_t &, ll, ll) >;
	//using update_f = function< void(structure_t &, ll, update_t) >;
	
	const merge_f f;
	const range_get_f g;
	const update_f h;
	const get_t identity;
	ll sz;
	vector< structure_t > seg;
	vector< vector< ll > > LL, RR;
	vector< vector< ll > > beet;
	
	SegmentTree2DCompressed(ll n, const merge_f &f, const range_get_f &g, const update_f &h, const get_t &identity)
			: f(f), g(g), h(h), identity(identity) {
		sz = 1;
		while(sz < n) sz <<= 1;
		beet.resize(2 * sz);
		LL.resize(2 * sz);
		RR.resize(2 * sz);
	}

	get_t update(ll a, ll x, update_t z, ll k, ll l, ll r) {
		//if(r <= a || a + 1 <= l) return seg[k][x]; //???
		if(r <= a || a + 1 <= l) return identity;
		if(a <= l && r <= a + 1) { h(seg[k], x, z); return z; }
		get_t sum0 = update(a, LL[k][x], z, 2 * k + 0, l, (l + r) >> 1);
		get_t sum1 = update(a, RR[k][x], z, 2 * k + 1, (l + r) >> 1, r);
		get_t newsum = f(sum0, sum1);
		h(seg[k], x, newsum);
		return newsum;
	}

	void update(ll x, ll y, update_t z) {
		y = lower_bound(begin(beet[1]), end(beet[1]), y) - begin(beet[1]);
		update(x, y, z, 1, 0, sz);
	}

	get_t query(ll a, ll b, ll x, ll y, ll k, ll l, ll r) {
		if(a >= r || b <= l) return identity;
		if(a <= l && r <= b) return g(seg[k], x, y);
		return f(query(a, b, LL[k][x], LL[k][y], 2 * k + 0, l, (l + r) >> 1),
				 query(a, b, RR[k][x], RR[k][y], 2 * k + 1, (l + r) >> 1, r));
	}

	get_t query(ll a, ll b, ll x, ll y) {
		x = lower_bound(begin(beet[1]), end(beet[1]), x) - begin(beet[1]);
		y = lower_bound(begin(beet[1]), end(beet[1]), y) - begin(beet[1]);
		return query(a, b, x, y, 1, 0, sz);
	}

	void build() {
		for(ll k = beet.size() - 1; k >= sz; k--) {
			sort(begin(beet[k]), end(beet[k]));
			beet[k].erase(unique(begin(beet[k]), end(beet[k])), end(beet[k]));
		}
		for(ll k = sz - 1; k > 0; k--) {
			beet[k].resize(beet[2 * k + 0].size() + beet[2 * k + 1].size());
			merge(begin(beet[2 * k + 0]), end(beet[2 * k + 0]), begin(beet[2 * k + 1]), end(beet[2 * k + 1]), begin(beet[k]));
			beet[k].erase(unique(begin(beet[k]), end(beet[k])), end(beet[k]));
			LL[k].resize(beet[k].size() + 1);
			RR[k].resize(beet[k].size() + 1);
			ll tail1 = 0, tail2 = 0;
			for(ll i = 0; i < (ll)beet[k].size(); i++) {
				while(tail1 < (ll)beet[2 * k + 0].size() && beet[2 * k + 0][tail1] < beet[k][i]) ++tail1;
				while(tail2 < (ll)beet[2 * k + 1].size() && beet[2 * k + 1][tail2] < beet[k][i]) ++tail2;
				LL[k][i] = tail1, RR[k][i] = tail2;
			}
			LL[k][beet[k].size()] = (ll) beet[2 * k + 0].size();
			RR[k][beet[k].size()] = (ll) beet[2 * k + 1].size();
		}
		seg.reserve(beet.size());
		for(ll k = 0; k < (ll)beet.size(); k++) {
			seg.emplace_back(beet[k].size(), f, identity);
		}
	}

	void preupdate(ll x, ll y) {
		beet[x + sz].push_back(y);
	}
};
template< typename structure_t, typename get_t, typename update_t, typename merge_f, typename range_get_f, typename update_f>
std::ostream& operator<<(std::ostream& s, SegmentTree2DCompressed<structure_t,get_t,update_t,merge_f,range_get_f,update_f> seg) {
	s << "\\\n";
	for(ll i=0; i<seg.sz; i++) for(ll j=0; j<seg.sz; j++) s << seg.query(i, i+1, j, j+1) << "\t\n"[j==seg.sz-1];
	return s;
}

/*-----8<-----library-----8<-----*/

void solve() {
	ll N, M, Q;
	cin >> N >> M >> Q;
	vector<ll> A(Q), B(Q);
	rep(i, Q) cin >> A[i] >> B[i], A[i]--, B[i]--;

	//矩形max/min
	//矩形addはできないのでBIT版を使ってください
	//auto fF = [](ll x, ll y){ return max(x, y); }; //0LL
	auto fF = [](ll x, ll y){ return max(x, y); }; //INF
	using Seg = SegmentTree<ll, decltype(fF)>;
	auto fG = [](Seg &s, ll x, ll y) { return s.query(x, y); };
	auto fH = [](Seg &s, ll k, ll x) { s.update(k, x); };
	//サイズ変更忘れないこと
	SegmentTree2DCompressed< Seg, ll, ll, decltype(fF), decltype(fG), decltype(fH) > seg(max(N,M)+1, fF, fG, fH, 0);
	//seg.update(l,r,x); は xに置換 する点に注意

	for(auto&& [a,b]:zip(A,B)) {
		seg.preupdate(a, b);
	}
	seg.build();

	for(auto&& [a,b]:zip(A,B)){
		ll t = seg.query(0, a, 0, b);
		seg.update(a, b, t + 1);
	}
	ll ans = seg.query(0, N, 0, M);
	p(ans);
}

signed main() {
#ifndef LOCAL_DEV
	//std::cin.tie(nullptr);
	//std::ios::sync_with_stdio(false);
#endif
	//ll Q; cin >> Q; while(Q--)solve();
	solve();
	return 0;
}