#include <algorithm>  
#include <iostream>  
#include <sstream>  
#include <string>  
#include <vector>  
#include <queue>  
#include <set>  
#include <map>  
#include <cstdio>  
#include <cstdlib>  
#include <cctype>  
#include <cmath>  
#include <cstring>
#include <list>  
#include <cassert>
#include <climits>
#include <bitset>
#include <chrono>
#include <random>
using namespace std;

#define PB push_back  
#define MP make_pair  
#define SZ(v) ((int)(v).size())  
#define FOR(i,a,b) for(int i=(a);i<(b);++i)  
#define REP(i,n) FOR(i,0,n)  
#define FORE(i,a,b) for(int i=(a);i<=(b);++i)  
#define REPE(i,n) FORE(i,0,n)  
#define FORSZ(i,a,v) FOR(i,a,SZ(v))  
#define REPSZ(i,v) REP(i,SZ(v))  
std::mt19937 rnd((int)std::chrono::steady_clock::now().time_since_epoch().count());
typedef long long ll;
ll gcd(ll a, ll b) { return b == 0 ? a : gcd(b, a % b); }

template<typename Item, typename Sum, typename Lazy> struct SplayTree {
	struct Node { int par, ch[2]; Item item; Sum sum; Lazy lazy; Node(Item item, Sum sum, Lazy lazy) :par(-1), item(item), sum(sum), lazy(lazy) { ch[0] = ch[1] = -1; } };
	vector<Node> nodes;

	void reset() { nodes.clear(); }
	void apply(int x, Lazy lazy) { nodes[x].item += lazy; nodes[x].sum += lazy; nodes[x].lazy += lazy; }
	void push(int x) { REP(z, 2) if (nodes[x].ch[z] != -1) apply(nodes[x].ch[z], nodes[x].lazy); nodes[x].lazy = Lazy(); }
	void update(int x) { nodes[x].sum = Sum(); if (nodes[x].ch[0] != -1) nodes[x].sum += nodes[nodes[x].ch[0]].sum; nodes[x].sum += Sum(nodes[x].item); if (nodes[x].ch[1] != -1) nodes[x].sum += nodes[nodes[x].ch[1]].sum; }
	void connect(int x, int p, int z) { if (x != -1) nodes[x].par = p; if (p != -1) nodes[p].ch[z] = x; }
	int disconnect(int p, int z) { int x = nodes[p].ch[z]; nodes[p].ch[z] = -1; if (x != -1) nodes[x].par = -1; return x; }
	void rotate(int x) {
		int p = nodes[x].par, g = nodes[p].par, z = nodes[p].ch[0] == x ? 0 : 1, y = nodes[x].ch[1 - z]; push(p), push(x);
		connect(y, p, z), connect(p, x, 1 - z), connect(x, g, g == -1 ? -1 : nodes[g].ch[0] == p ? 0 : 1); update(p);
	}
	void splay(int x, int y = -1) { if (nodes[x].par == y) return; while (nodes[x].par != y) { int p = nodes[x].par, g = nodes[p].par; if (g != y) rotate((nodes[p].ch[0] == x) == (nodes[g].ch[0] == p) ? p : x); rotate(x); } update(x); }
	int first(int x) { if (x == -1) return x; splay(x); while (nodes[x].ch[0] != -1) x = nodes[x].ch[0]; splay(x); return x; }
	int last(int x) { if (x == -1) return x; splay(x); while (nodes[x].ch[1] != -1) x = nodes[x].ch[1]; splay(x); return x; }

	int add(Item item) { nodes.PB(Node(item, Sum(item), Lazy())); return SZ(nodes) - 1; };
	int join(int l, int r) { if (l == -1) return r;	l = last(l); push(l); connect(r, l, 1); update(l); return l; }
	void split(int x, int v, int& l, int& r) {
		if (x == -1) { l = r = -1; return; } else splay(x);
		l = r = -1;
		while (x != -1) { push(x); if (nodes[x].item.l() < v) l = x, x = nodes[x].ch[1]; else r = x, x = nodes[x].ch[0]; }
		if (l != -1) splay(l); if (r != -1) splay(r, l);
		if (l == -1) return;
		assert(nodes[l].par == -1 && nodes[l].ch[1] == r && (r == -1 || nodes[r].ch[0] == -1));
		push(l); disconnect(l, 1); update(l);
		if (nodes[l].item.r() < v) return;
		Item splitted = nodes[l].item.split(v);
		if (nodes[l].ch[0] != -1 && nodes[nodes[l].ch[0]].item.r() == nodes[l].item.r()) l = disconnect(l, 0);
		if (r == -1 || splitted.l() != nodes[r].item.l()) r = join(add(splitted), r);
		update(l);
	}
	void gather(int x, vector<Item>& ret) { push(x); if (nodes[x].ch[0] != -1) gather(nodes[x].ch[0], ret); ret.PB(nodes[x].item); if (nodes[x].ch[1] != -1) gather(nodes[x].ch[1], ret); }
	vector<Item> all(int x) { vector<Item> ret; if (x != -1) splay(x), gather(x, ret); return ret; }
};

const int MAXRECT = 200000;
const int INF = 1000000000;
struct Rect { int lt, rt, lx, rx; };

int nrect, sx;
Rect rect[MAXRECT];

struct Line {
	int ly, ry, lcost, slope;
	Line() {}
	Line(int ly, int ry, int lcost, int slope) :ly(ly), ry(ry), lcost(lcost), slope(ly == ry ? 0 : slope) {}
	int rcost() { return lcost + slope * (ry - ly); }
	int len() { return ry - ly; }
	void setly(int nly) { lcost += (nly - ly) * slope; ly = nly; if (ly == ry) slope = 0; }
	void setry(int nry) { ry = nry; if (ly == ry) slope = 0; }
	int l() { return ly; }
	int r() { return ry; }
	Line split(int y) {
		assert(ly < y && y <= ry);
		auto ret = Line(y, ry, lcost + (y - ly) * slope, slope);
		setry(y - 1);
		return ret;
	}
};
struct SumLine { SumLine() {} SumLine(Line line) {} };
SumLine& operator+=(SumLine& a, const SumLine& b) { return a; }
struct LazyLine {};
Line& operator+=(Line& a, const LazyLine& b) { return a; }
SumLine& operator+=(SumLine& a, const LazyLine& b) { return a; }
LazyLine& operator+=(LazyLine& a, const LazyLine& b) { return a; }

SplayTree<Line, SumLine, LazyLine> linetree;

void printfunc(int lineroot,int tline) {
	if (lineroot == -1) {
		printf(" BLOCKED");
	} else {
		auto alllines = linetree.all(lineroot);
		for (auto line : alllines) printf(" (%d,%d)..(%d,%d)", line.ly == -INF ? -INF : line.ly + tline, line.ly == -INF ? INF : line.lcost, line.ry == +INF ? +INF : line.ry + tline, line.ry == +INF ? INF : line.rcost());
	}
	puts("");
}

int t;

int rtrimfunc(int node, int nry) {
	while(true) {
		node = linetree.last(node);
		if (linetree.nodes[node].item.ry <= nry) break;
		if (linetree.nodes[node].item.ly < nry || linetree.nodes[node].item.ly == nry && linetree.nodes[node].ch[0] == -1) {
			linetree.nodes[node].item.setry(nry);
			break;
		}
		node = linetree.disconnect(node, 0);
		assert(node != -1);
	}
	return node;
}
int lgrowfunc(int node, int nly) {
	node = linetree.first(node);
	assert(nly <= linetree.nodes[node].item.ly);
	if (nly == linetree.nodes[node].item.ly) return node;
	if (linetree.nodes[node].item.slope == -1 || linetree.nodes[node].item.ly == linetree.nodes[node].item.ry) {
		linetree.nodes[node].item.slope = -1;
		linetree.nodes[node].item.setly(nly);
		linetree.update(node);
	} else {
		Line line(nly, linetree.nodes[node].item.ly, linetree.nodes[node].item.lcost + linetree.nodes[node].item.ly - nly, -1);
		node = linetree.join(linetree.add(line), node);
	}
	return node;
}
int rgrowfunc(int node, int nry) {
	node = linetree.last(node);
	assert(nry >= linetree.nodes[node].item.ry);
	if (nry == linetree.nodes[node].item.ry) return node;
	if (linetree.nodes[node].item.slope == +1 || linetree.nodes[node].item.ly == linetree.nodes[node].item.ry) {
		linetree.nodes[node].item.slope = +1;
		linetree.nodes[node].item.setry(nry);
		linetree.update(node);
	} else {
		Line line(linetree.nodes[node].item.ry, nry, linetree.nodes[node].item.rcost(), +1);
		node = linetree.join(node, linetree.add(line));
	}
	return node;
}
int shiftfunc(int node, int dt) {
	if (dt == 0) return node;
	node = linetree.first(node);
	int ply = linetree.nodes[node].item.ly;
	if (ply != -INF) node = lgrowfunc(node, ply - dt);
	node = linetree.last(node);
	int pry = linetree.nodes[node].item.ry;
	if (pry != +INF) node = rtrimfunc(node, pry - dt);
	return node;
}
int mergefunc(int l, int r) {
	//printf("merging\n");
	//printfunc(l, t);
	//printfunc(r, t);
	l = linetree.last(l);
	r = linetree.first(r);
	while (l != -1 && r != -1 && linetree.nodes[l].item.rcost() > linetree.nodes[r].item.lcost) {
		assert(linetree.nodes[l].item.ry == linetree.nodes[r].item.ly);
		if (linetree.nodes[l].item.slope == -1 || linetree.nodes[l].item.ly == linetree.nodes[l].item.ry) {
			r = lgrowfunc(r, linetree.nodes[l].item.ly);
			l = linetree.disconnect(l, 0);
		} else {
			assert(linetree.nodes[l].item.slope == 1);
			if (linetree.nodes[r].item.lcost + linetree.nodes[l].item.len() <= linetree.nodes[l].item.lcost) {
				r = lgrowfunc(r, linetree.nodes[l].item.ly);
				l = linetree.disconnect(l, 0);
			} else {
				int y = linetree.nodes[r].item.lcost - linetree.nodes[l].item.lcost + linetree.nodes[l].item.ly + linetree.nodes[l].item.ry; assert(y % 2 == 0); y /= 2;
				assert(y > linetree.nodes[l].item.ly && y < linetree.nodes[l].item.ry);
				r = lgrowfunc(r, y);
				linetree.nodes[l].item.setry(y);
			}
		}
		l = linetree.last(l);
		r = linetree.first(r);
	}
	while (l != -1 && r != -1 && linetree.nodes[l].item.rcost() < linetree.nodes[r].item.lcost) {
		assert(linetree.nodes[l].item.ry == linetree.nodes[r].item.ly);
		if (linetree.nodes[r].item.slope == +1 || linetree.nodes[r].item.ly == linetree.nodes[r].item.ry) {
			l = rgrowfunc(l, linetree.nodes[r].item.ry);
			r = linetree.disconnect(r, 1);
		} else {
			assert(linetree.nodes[r].item.slope == -1);
			if (linetree.nodes[l].item.rcost() + linetree.nodes[r].item.len() <= linetree.nodes[r].item.rcost()) {
				l = rgrowfunc(l, linetree.nodes[r].item.ry);
				r = linetree.disconnect(r, 1);
			} else {
				int y = linetree.nodes[r].item.rcost() - linetree.nodes[l].item.rcost() + linetree.nodes[r].item.ly + linetree.nodes[r].item.ry; assert(y % 2 == 0); y /= 2;
				assert(y > linetree.nodes[r].item.ly && y < linetree.nodes[r].item.ry);
				l = rgrowfunc(l, y);
				linetree.nodes[r].item.setly(y);
			}
		}
		l = linetree.last(l);
		r = linetree.first(r);
	}
	int ret = linetree.join(l, r);
	//printf("-> "); printfunc(ret, t);
	return ret;
}

struct Region {
	int lx, rx, blockcnt, lineroot, tline;
	Region(int lx, int rx, int blockcnt, int lineroot, int tline) :lx(lx), rx(rx), blockcnt(blockcnt), lineroot(lineroot), tline(tline) {};
	int l() { return lx; }
	int r() { return rx; }
	void norm() { if (lineroot != -1) { lineroot = shiftfunc(lineroot, t - tline); tline = t; } }
	Region split(int x) {
		assert(lx < x && x <= rx); 
		norm();
		auto ret = Region(x, rx, blockcnt, -1, tline);
		rx = x - 1;
		if (lineroot != -1) linetree.split(lineroot, x - t, lineroot, ret.lineroot);
		return ret;
	};
};
struct SumRegion {
	int mnblockcnt;
	SumRegion() { mnblockcnt = INT_MAX; }
	SumRegion(Region region) { mnblockcnt = region.lineroot == -1 ? INT_MAX : region.blockcnt; }
};
SumRegion& operator+=(SumRegion& a, const SumRegion& b) { a.mnblockcnt = min(a.mnblockcnt, b.mnblockcnt); return a; }
struct LazyRegion {
	int lazyblockcnt;
	LazyRegion() { lazyblockcnt = 0; }
	LazyRegion(int lazyblockcnt) :lazyblockcnt(lazyblockcnt) {}
};
Region& operator+=(Region& a, const LazyRegion& b) { a.blockcnt += b.lazyblockcnt; return a; }
SumRegion& operator+=(SumRegion& a, const LazyRegion& b) { if (a.mnblockcnt != INT_MAX) a.mnblockcnt += b.lazyblockcnt; return a; }
LazyRegion& operator+=(LazyRegion& a, const LazyRegion& b) { a.lazyblockcnt += b.lazyblockcnt; return a; }


SplayTree<Region, SumRegion, LazyRegion> regiontree;

void print(int regionroot) {
	auto allregions = regiontree.all(regionroot);
	for (auto region : allregions) {
		//region.norm();
		printf("[%d..%d] = %d:", region.lx, region.rx, region.blockcnt); if (region.lineroot!=-1 && region.tline != t) printf(" (delay %d)", t - region.tline);
		printfunc(region.lineroot, region.tline);
	}
}

int killzeroes(int node) {
	regiontree.splay(node);
	while (regiontree.nodes[node].sum.mnblockcnt == 0) {
		//printf("killing\n"); print(node);
		while (regiontree.nodes[node].item.blockcnt != 0 || regiontree.nodes[node].item.lineroot == -1) {
			//printf("node=%d\n", node);
			if (regiontree.nodes[node].ch[0] != -1 && regiontree.nodes[regiontree.nodes[node].ch[0]].sum.mnblockcnt == 0) {
				node = regiontree.nodes[node].ch[0];
			} else {
				node = regiontree.nodes[node].ch[1];
			}
			assert(node != -1 && regiontree.nodes[node].sum.mnblockcnt == 0);
		}
		//printf("found node=%d\n", node);
		assert(regiontree.nodes[node].item.lineroot != -1);
		regiontree.splay(node);
		regiontree.nodes[node].item.lineroot = -1;
		regiontree.update(node);
	}
	return node;
}

int rgrow(int node, int x) {
	int l, r; regiontree.split(node, x + 1, l, r);
	l = regiontree.last(l);
	r = regiontree.first(r);
	//printf("growing\n");
	//printf("l\n"); print(l);
	//printf("r\n"); print(r);
	if (l == -1 || regiontree.nodes[l].item.lineroot == -1) return regiontree.join(l, r);
	while (r != -1 && regiontree.nodes[r].item.lineroot == -1 && regiontree.nodes[r].item.blockcnt == 0) {
		//printf("step\n");
		assert(regiontree.nodes[l].item.rx + 1 == regiontree.nodes[r].item.lx);
		regiontree.nodes[l].item.rx = regiontree.nodes[r].item.rx;
		r = regiontree.disconnect(r, 1);
		r = regiontree.first(r);
	}
	if (r != -1 && regiontree.nodes[r].item.lineroot != -1) {
		assert(regiontree.nodes[l].item.rx + 1 == regiontree.nodes[r].item.lx);
		regiontree.nodes[l].item.rx = regiontree.nodes[r].item.lx;
		regiontree.nodes[l].item.norm();
		regiontree.nodes[l].item.lineroot = rgrowfunc(regiontree.nodes[l].item.lineroot, regiontree.nodes[l].item.rx - t);
		regiontree.nodes[r].item.norm();
		regiontree.nodes[l].item.lineroot = mergefunc(regiontree.nodes[l].item.lineroot, regiontree.nodes[r].item.lineroot);
		regiontree.nodes[l].item.rx = regiontree.nodes[r].item.rx;
		r = regiontree.disconnect(r, 1);
	} else {
		regiontree.nodes[l].item.norm();
		regiontree.nodes[l].item.lineroot = rgrowfunc(regiontree.nodes[l].item.lineroot, regiontree.nodes[l].item.rx - t);
	}
	int ret = regiontree.join(l, r);
	//printf("after rgrow\n"); print(ret);
	return ret;
}

int lgrow(int node, int x) {
	//printf("lgrow %d\n", x);
	int l, r; regiontree.split(node, x, l, r);
	l = regiontree.last(l);
	r = regiontree.first(r);
	if (r == -1 || regiontree.nodes[r].item.lineroot == -1) return regiontree.join(l, r);
	while (l != -1 && regiontree.nodes[l].item.lineroot == -1 && regiontree.nodes[l].item.blockcnt == 0) {
		assert(regiontree.nodes[l].item.rx + 1 == regiontree.nodes[r].item.lx);
		regiontree.nodes[r].item.lx = regiontree.nodes[l].item.lx;
		l = regiontree.disconnect(l, 0);
		l = regiontree.last(l);
	}
	if (l != -1 && regiontree.nodes[l].item.lineroot != -1) {
		assert(regiontree.nodes[l].item.rx + 1 == regiontree.nodes[r].item.lx);
		regiontree.nodes[l].item.rx = regiontree.nodes[r].item.lx;
		regiontree.nodes[l].item.norm();
		regiontree.nodes[l].item.lineroot = rgrowfunc(regiontree.nodes[l].item.lineroot, regiontree.nodes[l].item.rx - t);
		regiontree.nodes[r].item.norm();
		regiontree.nodes[l].item.lineroot = mergefunc(regiontree.nodes[l].item.lineroot, regiontree.nodes[r].item.lineroot);
		regiontree.nodes[l].item.rx = regiontree.nodes[r].item.rx;
		r = regiontree.disconnect(r, 1);
	} else {
		regiontree.nodes[r].item.norm();
		regiontree.nodes[r].item.lineroot = lgrowfunc(regiontree.nodes[r].item.lineroot, regiontree.nodes[r].item.lx - t);
	}
	return regiontree.join(l, r);
}

int solve() {
	//REP(i, nrect) printf("t=%d..%d y=%d..%d to %d..%d\n", rect[i].lt, rect[i].rt, rect[i].lx - rect[i].lt, rect[i].rx - rect[i].lt, rect[i].lx - rect[i].rt, rect[i].rx - rect[i].rt);

	linetree.reset();
	regiontree.reset();
	int linedn = linetree.add(Line(-INF, sx, abs(-INF - sx), -1));
	int lineup = linetree.add(Line(sx, +INF, 0, +1));
	int lineroot = linetree.join(linedn, lineup);
	int regionroot = regiontree.add(Region(-INF, +INF, 0, lineroot, 0));

	vector<pair<int, int>> e;
	REP(i, nrect) e.PB(MP(2 * rect[i].lt + 1, i)), e.PB(MP(2 * rect[i].rt + 0, i));
	sort(e.begin(), e.end());
	//printf("INITIAL\n"); print(regionroot);
	REPSZ(i, e) {
		t = e[i].first >> 1; int kind = e[i].first & 1, idx = e[i].second;
		if (kind == 0) { // release rect
			int l, m, r;
			regiontree.split(regionroot, rect[idx].lx + 1, l, m);
			regiontree.split(m, rect[idx].rx, m, r);
			regiontree.apply(m, LazyRegion(-1));
			regionroot = regiontree.join(regiontree.join(l, m), r);
			regionroot = rgrow(regionroot, rect[idx].lx);
			regionroot = lgrow(regionroot, rect[idx].rx);
		}
		if (kind == 1) { // block rect
			int l, m, r;
			regiontree.split(regionroot, rect[idx].lx + 1, l, m);
			//printf("L\n"); print(l);
			//printf("M\n"); print(m);
			regiontree.split(m, rect[idx].rx, m, r);
			//printf("M\n"); print(m);
			//printf("R\n"); print(r);
			m = killzeroes(m);
			//printf("M\n"); print(m);
			regiontree.apply(m, LazyRegion(1));
			regionroot = regiontree.join(regiontree.join(l, m), r);
		}
		//printf("after %s rect %d (t=%d)\n", kind == 0 ? "releasing" : "blocking", idx + 1, t); print(regionroot);
		//if (i == 0) exit(0);
	}
	//printf("FINAL (t=%d)\n",t); print(regionroot);

	auto finalregions = regiontree.all(regionroot);
	assert(SZ(finalregions) == 1);
	auto finalregion = finalregions[0];
	finalregion.norm();
	assert(finalregion.lineroot != -1);
	auto finalfunc = linetree.all(finalregion.lineroot);
	int ret = INT_MAX;
	for (auto func : finalfunc) ret = min(ret, min(func.lcost, func.rcost()));
	return ret;
}

void run() {
	scanf("%d", &nrect);
	scanf("%d", &sx);
	REP(i, nrect) scanf("%d%d%d%d", &rect[i].lt, &rect[i].rt, &rect[i].lx, &rect[i].rx), --rect[i].lt, ++rect[i].rt, --rect[i].lx, ++rect[i].rx;
	printf("%d\n", solve());
}

void stress() {
	int mxrect = 100, mxdim = 100;
	REP(rep, 10000) {
		nrect = rnd() % mxrect + 1;
		int tdim = rnd() % mxdim + 1;
		int xdim = rnd() % mxdim + 1;
		sx = rnd() % (xdim + 1);
		REP(i, nrect) {
			rect[i].lt = rnd() % tdim; rect[i].rt = rnd() % tdim; if (rect[i].lt > rect[i].rt) swap(rect[i].lt, rect[i].rt); rect[i].rt += 2;
			rect[i].lx = rnd() % xdim; rect[i].rx = rnd() % xdim; if (rect[i].lx > rect[i].rx) swap(rect[i].lx, rect[i].rx); rect[i].rx += 2;
		}
		//printf("%d\n%d\n", nrect, sx); REP(i, nrect) printf("%d %d %d %d\n", rect[i].lt + 1, rect[i].rt - 1, rect[i].lx + 1, rect[i].rx - 1);
		solve();
		printf(".");
	}
}

int main() {
	run();
	//stress();
	return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

Note that the differences between easy and hard versions are the constraints on n and the time limit. You can make hacks only if both versions are solved.

AquaMoon knew through foresight that some ghosts wanted to curse tourists on a pedestrian street. But unfortunately, this time, these ghosts were hiding in a barrier, and she couldn't enter this barrier in a short time and destroy them. Therefore, all that can be done is to save any unfortunate person on the street from the ghosts.

The pedestrian street can be represented as a one-dimensional coordinate system. There is one person hanging out on the pedestrian street. At the time 0 he is at coordinate x, moving with a speed of 1 unit per second. In particular, at time i the person will be at coordinate x+i.

The ghosts are going to cast n curses on the street. The i-th curse will last from time tl_i-1+10^{-18} to time tr_i+1-10^{-18} (exclusively) and will kill people with coordinates from l_i-1+10^{-18} to r_i+1-10^{-18} (exclusively). Formally that means, that the person, whose coordinate is between (l_i-1+10^{-18},r_i+1-10^{-18}) in the time range (tl_i-1+10^{-18},tr_i+1-10^{-18}) will die.

To save the person on the street, AquaMoon can stop time at any moment t, and then move the person from his current coordinate x to any coordinate y (t, x and y are not necessarily integers). The movement costs AquaMoon |x-y| energy. The movement is continuous, so if there exists some cursed area between points x and y at time t, the person will die too.

AquaMoon wants to know what is the minimum amount of energy she needs to spend in order to save the person on the street from all n curses. But she is not good at programming. As her friend, can you help her?

Input

The first line contains a single integer n (1≤ n≤ 2 ⋅ 10^5) — the number of curses.

The next line contains a single integer x (1≤ x≤ 10^6) — the initial coordinate of the person.

The following n lines contain four integers tl_i, tr_i, l_i, r_i each (1≤ tl_i≤ tr_i≤ 10^6, 1≤ l_i≤ r_i≤ 10^6).

Output

Print a single integer — the minimum energy which AquaMoon needs to spent, rounded up to the nearest integer (in case there are two nearest integers you should round the answer to the highest of them).

Examples

Input


2
1
1 2 1 2
2 3 2 3


Output


2

Input


3
4
1 4 1 2
1 4 4 15
6 7 1 4


Output


8

Input


4
3
1 5 1 1
4 10 1 4
1 2 3 13
1 10 7 19


Output


14

Input


7
5
78 96 76 91
6 16 18 37
53 63 40 56
83 88 21 38
72 75 17 24
63 63 53 60
34 46 60 60


Output


20

### Response

```cpp
#include <algorithm>  
#include <iostream>  
#include <sstream>  
#include <string>  
#include <vector>  
#include <queue>  
#include <set>  
#include <map>  
#include <cstdio>  
#include <cstdlib>  
#include <cctype>  
#include <cmath>  
#include <cstring>
#include <list>  
#include <cassert>
#include <climits>
#include <bitset>
#include <chrono>
#include <random>
using namespace std;

#define PB push_back  
#define MP make_pair  
#define SZ(v) ((int)(v).size())  
#define FOR(i,a,b) for(int i=(a);i<(b);++i)  
#define REP(i,n) FOR(i,0,n)  
#define FORE(i,a,b) for(int i=(a);i<=(b);++i)  
#define REPE(i,n) FORE(i,0,n)  
#define FORSZ(i,a,v) FOR(i,a,SZ(v))  
#define REPSZ(i,v) REP(i,SZ(v))  
std::mt19937 rnd((int)std::chrono::steady_clock::now().time_since_epoch().count());
typedef long long ll;
ll gcd(ll a, ll b) { return b == 0 ? a : gcd(b, a % b); }

template<typename Item, typename Sum, typename Lazy> struct SplayTree {
	struct Node { int par, ch[2]; Item item; Sum sum; Lazy lazy; Node(Item item, Sum sum, Lazy lazy) :par(-1), item(item), sum(sum), lazy(lazy) { ch[0] = ch[1] = -1; } };
	vector<Node> nodes;

	void reset() { nodes.clear(); }
	void apply(int x, Lazy lazy) { nodes[x].item += lazy; nodes[x].sum += lazy; nodes[x].lazy += lazy; }
	void push(int x) { REP(z, 2) if (nodes[x].ch[z] != -1) apply(nodes[x].ch[z], nodes[x].lazy); nodes[x].lazy = Lazy(); }
	void update(int x) { nodes[x].sum = Sum(); if (nodes[x].ch[0] != -1) nodes[x].sum += nodes[nodes[x].ch[0]].sum; nodes[x].sum += Sum(nodes[x].item); if (nodes[x].ch[1] != -1) nodes[x].sum += nodes[nodes[x].ch[1]].sum; }
	void connect(int x, int p, int z) { if (x != -1) nodes[x].par = p; if (p != -1) nodes[p].ch[z] = x; }
	int disconnect(int p, int z) { int x = nodes[p].ch[z]; nodes[p].ch[z] = -1; if (x != -1) nodes[x].par = -1; return x; }
	void rotate(int x) {
		int p = nodes[x].par, g = nodes[p].par, z = nodes[p].ch[0] == x ? 0 : 1, y = nodes[x].ch[1 - z]; push(p), push(x);
		connect(y, p, z), connect(p, x, 1 - z), connect(x, g, g == -1 ? -1 : nodes[g].ch[0] == p ? 0 : 1); update(p);
	}
	void splay(int x, int y = -1) { if (nodes[x].par == y) return; while (nodes[x].par != y) { int p = nodes[x].par, g = nodes[p].par; if (g != y) rotate((nodes[p].ch[0] == x) == (nodes[g].ch[0] == p) ? p : x); rotate(x); } update(x); }
	int first(int x) { if (x == -1) return x; splay(x); while (nodes[x].ch[0] != -1) x = nodes[x].ch[0]; splay(x); return x; }
	int last(int x) { if (x == -1) return x; splay(x); while (nodes[x].ch[1] != -1) x = nodes[x].ch[1]; splay(x); return x; }

	int add(Item item) { nodes.PB(Node(item, Sum(item), Lazy())); return SZ(nodes) - 1; };
	int join(int l, int r) { if (l == -1) return r;	l = last(l); push(l); connect(r, l, 1); update(l); return l; }
	void split(int x, int v, int& l, int& r) {
		if (x == -1) { l = r = -1; return; } else splay(x);
		l = r = -1;
		while (x != -1) { push(x); if (nodes[x].item.l() < v) l = x, x = nodes[x].ch[1]; else r = x, x = nodes[x].ch[0]; }
		if (l != -1) splay(l); if (r != -1) splay(r, l);
		if (l == -1) return;
		assert(nodes[l].par == -1 && nodes[l].ch[1] == r && (r == -1 || nodes[r].ch[0] == -1));
		push(l); disconnect(l, 1); update(l);
		if (nodes[l].item.r() < v) return;
		Item splitted = nodes[l].item.split(v);
		if (nodes[l].ch[0] != -1 && nodes[nodes[l].ch[0]].item.r() == nodes[l].item.r()) l = disconnect(l, 0);
		if (r == -1 || splitted.l() != nodes[r].item.l()) r = join(add(splitted), r);
		update(l);
	}
	void gather(int x, vector<Item>& ret) { push(x); if (nodes[x].ch[0] != -1) gather(nodes[x].ch[0], ret); ret.PB(nodes[x].item); if (nodes[x].ch[1] != -1) gather(nodes[x].ch[1], ret); }
	vector<Item> all(int x) { vector<Item> ret; if (x != -1) splay(x), gather(x, ret); return ret; }
};

const int MAXRECT = 200000;
const int INF = 1000000000;
struct Rect { int lt, rt, lx, rx; };

int nrect, sx;
Rect rect[MAXRECT];

struct Line {
	int ly, ry, lcost, slope;
	Line() {}
	Line(int ly, int ry, int lcost, int slope) :ly(ly), ry(ry), lcost(lcost), slope(ly == ry ? 0 : slope) {}
	int rcost() { return lcost + slope * (ry - ly); }
	int len() { return ry - ly; }
	void setly(int nly) { lcost += (nly - ly) * slope; ly = nly; if (ly == ry) slope = 0; }
	void setry(int nry) { ry = nry; if (ly == ry) slope = 0; }
	int l() { return ly; }
	int r() { return ry; }
	Line split(int y) {
		assert(ly < y && y <= ry);
		auto ret = Line(y, ry, lcost + (y - ly) * slope, slope);
		setry(y - 1);
		return ret;
	}
};
struct SumLine { SumLine() {} SumLine(Line line) {} };
SumLine& operator+=(SumLine& a, const SumLine& b) { return a; }
struct LazyLine {};
Line& operator+=(Line& a, const LazyLine& b) { return a; }
SumLine& operator+=(SumLine& a, const LazyLine& b) { return a; }
LazyLine& operator+=(LazyLine& a, const LazyLine& b) { return a; }

SplayTree<Line, SumLine, LazyLine> linetree;

void printfunc(int lineroot,int tline) {
	if (lineroot == -1) {
		printf(" BLOCKED");
	} else {
		auto alllines = linetree.all(lineroot);
		for (auto line : alllines) printf(" (%d,%d)..(%d,%d)", line.ly == -INF ? -INF : line.ly + tline, line.ly == -INF ? INF : line.lcost, line.ry == +INF ? +INF : line.ry + tline, line.ry == +INF ? INF : line.rcost());
	}
	puts("");
}

int t;

int rtrimfunc(int node, int nry) {
	while(true) {
		node = linetree.last(node);
		if (linetree.nodes[node].item.ry <= nry) break;
		if (linetree.nodes[node].item.ly < nry || linetree.nodes[node].item.ly == nry && linetree.nodes[node].ch[0] == -1) {
			linetree.nodes[node].item.setry(nry);
			break;
		}
		node = linetree.disconnect(node, 0);
		assert(node != -1);
	}
	return node;
}
int lgrowfunc(int node, int nly) {
	node = linetree.first(node);
	assert(nly <= linetree.nodes[node].item.ly);
	if (nly == linetree.nodes[node].item.ly) return node;
	if (linetree.nodes[node].item.slope == -1 || linetree.nodes[node].item.ly == linetree.nodes[node].item.ry) {
		linetree.nodes[node].item.slope = -1;
		linetree.nodes[node].item.setly(nly);
		linetree.update(node);
	} else {
		Line line(nly, linetree.nodes[node].item.ly, linetree.nodes[node].item.lcost + linetree.nodes[node].item.ly - nly, -1);
		node = linetree.join(linetree.add(line), node);
	}
	return node;
}
int rgrowfunc(int node, int nry) {
	node = linetree.last(node);
	assert(nry >= linetree.nodes[node].item.ry);
	if (nry == linetree.nodes[node].item.ry) return node;
	if (linetree.nodes[node].item.slope == +1 || linetree.nodes[node].item.ly == linetree.nodes[node].item.ry) {
		linetree.nodes[node].item.slope = +1;
		linetree.nodes[node].item.setry(nry);
		linetree.update(node);
	} else {
		Line line(linetree.nodes[node].item.ry, nry, linetree.nodes[node].item.rcost(), +1);
		node = linetree.join(node, linetree.add(line));
	}
	return node;
}
int shiftfunc(int node, int dt) {
	if (dt == 0) return node;
	node = linetree.first(node);
	int ply = linetree.nodes[node].item.ly;
	if (ply != -INF) node = lgrowfunc(node, ply - dt);
	node = linetree.last(node);
	int pry = linetree.nodes[node].item.ry;
	if (pry != +INF) node = rtrimfunc(node, pry - dt);
	return node;
}
int mergefunc(int l, int r) {
	//printf("merging\n");
	//printfunc(l, t);
	//printfunc(r, t);
	l = linetree.last(l);
	r = linetree.first(r);
	while (l != -1 && r != -1 && linetree.nodes[l].item.rcost() > linetree.nodes[r].item.lcost) {
		assert(linetree.nodes[l].item.ry == linetree.nodes[r].item.ly);
		if (linetree.nodes[l].item.slope == -1 || linetree.nodes[l].item.ly == linetree.nodes[l].item.ry) {
			r = lgrowfunc(r, linetree.nodes[l].item.ly);
			l = linetree.disconnect(l, 0);
		} else {
			assert(linetree.nodes[l].item.slope == 1);
			if (linetree.nodes[r].item.lcost + linetree.nodes[l].item.len() <= linetree.nodes[l].item.lcost) {
				r = lgrowfunc(r, linetree.nodes[l].item.ly);
				l = linetree.disconnect(l, 0);
			} else {
				int y = linetree.nodes[r].item.lcost - linetree.nodes[l].item.lcost + linetree.nodes[l].item.ly + linetree.nodes[l].item.ry; assert(y % 2 == 0); y /= 2;
				assert(y > linetree.nodes[l].item.ly && y < linetree.nodes[l].item.ry);
				r = lgrowfunc(r, y);
				linetree.nodes[l].item.setry(y);
			}
		}
		l = linetree.last(l);
		r = linetree.first(r);
	}
	while (l != -1 && r != -1 && linetree.nodes[l].item.rcost() < linetree.nodes[r].item.lcost) {
		assert(linetree.nodes[l].item.ry == linetree.nodes[r].item.ly);
		if (linetree.nodes[r].item.slope == +1 || linetree.nodes[r].item.ly == linetree.nodes[r].item.ry) {
			l = rgrowfunc(l, linetree.nodes[r].item.ry);
			r = linetree.disconnect(r, 1);
		} else {
			assert(linetree.nodes[r].item.slope == -1);
			if (linetree.nodes[l].item.rcost() + linetree.nodes[r].item.len() <= linetree.nodes[r].item.rcost()) {
				l = rgrowfunc(l, linetree.nodes[r].item.ry);
				r = linetree.disconnect(r, 1);
			} else {
				int y = linetree.nodes[r].item.rcost() - linetree.nodes[l].item.rcost() + linetree.nodes[r].item.ly + linetree.nodes[r].item.ry; assert(y % 2 == 0); y /= 2;
				assert(y > linetree.nodes[r].item.ly && y < linetree.nodes[r].item.ry);
				l = rgrowfunc(l, y);
				linetree.nodes[r].item.setly(y);
			}
		}
		l = linetree.last(l);
		r = linetree.first(r);
	}
	int ret = linetree.join(l, r);
	//printf("-> "); printfunc(ret, t);
	return ret;
}

struct Region {
	int lx, rx, blockcnt, lineroot, tline;
	Region(int lx, int rx, int blockcnt, int lineroot, int tline) :lx(lx), rx(rx), blockcnt(blockcnt), lineroot(lineroot), tline(tline) {};
	int l() { return lx; }
	int r() { return rx; }
	void norm() { if (lineroot != -1) { lineroot = shiftfunc(lineroot, t - tline); tline = t; } }
	Region split(int x) {
		assert(lx < x && x <= rx); 
		norm();
		auto ret = Region(x, rx, blockcnt, -1, tline);
		rx = x - 1;
		if (lineroot != -1) linetree.split(lineroot, x - t, lineroot, ret.lineroot);
		return ret;
	};
};
struct SumRegion {
	int mnblockcnt;
	SumRegion() { mnblockcnt = INT_MAX; }
	SumRegion(Region region) { mnblockcnt = region.lineroot == -1 ? INT_MAX : region.blockcnt; }
};
SumRegion& operator+=(SumRegion& a, const SumRegion& b) { a.mnblockcnt = min(a.mnblockcnt, b.mnblockcnt); return a; }
struct LazyRegion {
	int lazyblockcnt;
	LazyRegion() { lazyblockcnt = 0; }
	LazyRegion(int lazyblockcnt) :lazyblockcnt(lazyblockcnt) {}
};
Region& operator+=(Region& a, const LazyRegion& b) { a.blockcnt += b.lazyblockcnt; return a; }
SumRegion& operator+=(SumRegion& a, const LazyRegion& b) { if (a.mnblockcnt != INT_MAX) a.mnblockcnt += b.lazyblockcnt; return a; }
LazyRegion& operator+=(LazyRegion& a, const LazyRegion& b) { a.lazyblockcnt += b.lazyblockcnt; return a; }


SplayTree<Region, SumRegion, LazyRegion> regiontree;

void print(int regionroot) {
	auto allregions = regiontree.all(regionroot);
	for (auto region : allregions) {
		//region.norm();
		printf("[%d..%d] = %d:", region.lx, region.rx, region.blockcnt); if (region.lineroot!=-1 && region.tline != t) printf(" (delay %d)", t - region.tline);
		printfunc(region.lineroot, region.tline);
	}
}

int killzeroes(int node) {
	regiontree.splay(node);
	while (regiontree.nodes[node].sum.mnblockcnt == 0) {
		//printf("killing\n"); print(node);
		while (regiontree.nodes[node].item.blockcnt != 0 || regiontree.nodes[node].item.lineroot == -1) {
			//printf("node=%d\n", node);
			if (regiontree.nodes[node].ch[0] != -1 && regiontree.nodes[regiontree.nodes[node].ch[0]].sum.mnblockcnt == 0) {
				node = regiontree.nodes[node].ch[0];
			} else {
				node = regiontree.nodes[node].ch[1];
			}
			assert(node != -1 && regiontree.nodes[node].sum.mnblockcnt == 0);
		}
		//printf("found node=%d\n", node);
		assert(regiontree.nodes[node].item.lineroot != -1);
		regiontree.splay(node);
		regiontree.nodes[node].item.lineroot = -1;
		regiontree.update(node);
	}
	return node;
}

int rgrow(int node, int x) {
	int l, r; regiontree.split(node, x + 1, l, r);
	l = regiontree.last(l);
	r = regiontree.first(r);
	//printf("growing\n");
	//printf("l\n"); print(l);
	//printf("r\n"); print(r);
	if (l == -1 || regiontree.nodes[l].item.lineroot == -1) return regiontree.join(l, r);
	while (r != -1 && regiontree.nodes[r].item.lineroot == -1 && regiontree.nodes[r].item.blockcnt == 0) {
		//printf("step\n");
		assert(regiontree.nodes[l].item.rx + 1 == regiontree.nodes[r].item.lx);
		regiontree.nodes[l].item.rx = regiontree.nodes[r].item.rx;
		r = regiontree.disconnect(r, 1);
		r = regiontree.first(r);
	}
	if (r != -1 && regiontree.nodes[r].item.lineroot != -1) {
		assert(regiontree.nodes[l].item.rx + 1 == regiontree.nodes[r].item.lx);
		regiontree.nodes[l].item.rx = regiontree.nodes[r].item.lx;
		regiontree.nodes[l].item.norm();
		regiontree.nodes[l].item.lineroot = rgrowfunc(regiontree.nodes[l].item.lineroot, regiontree.nodes[l].item.rx - t);
		regiontree.nodes[r].item.norm();
		regiontree.nodes[l].item.lineroot = mergefunc(regiontree.nodes[l].item.lineroot, regiontree.nodes[r].item.lineroot);
		regiontree.nodes[l].item.rx = regiontree.nodes[r].item.rx;
		r = regiontree.disconnect(r, 1);
	} else {
		regiontree.nodes[l].item.norm();
		regiontree.nodes[l].item.lineroot = rgrowfunc(regiontree.nodes[l].item.lineroot, regiontree.nodes[l].item.rx - t);
	}
	int ret = regiontree.join(l, r);
	//printf("after rgrow\n"); print(ret);
	return ret;
}

int lgrow(int node, int x) {
	//printf("lgrow %d\n", x);
	int l, r; regiontree.split(node, x, l, r);
	l = regiontree.last(l);
	r = regiontree.first(r);
	if (r == -1 || regiontree.nodes[r].item.lineroot == -1) return regiontree.join(l, r);
	while (l != -1 && regiontree.nodes[l].item.lineroot == -1 && regiontree.nodes[l].item.blockcnt == 0) {
		assert(regiontree.nodes[l].item.rx + 1 == regiontree.nodes[r].item.lx);
		regiontree.nodes[r].item.lx = regiontree.nodes[l].item.lx;
		l = regiontree.disconnect(l, 0);
		l = regiontree.last(l);
	}
	if (l != -1 && regiontree.nodes[l].item.lineroot != -1) {
		assert(regiontree.nodes[l].item.rx + 1 == regiontree.nodes[r].item.lx);
		regiontree.nodes[l].item.rx = regiontree.nodes[r].item.lx;
		regiontree.nodes[l].item.norm();
		regiontree.nodes[l].item.lineroot = rgrowfunc(regiontree.nodes[l].item.lineroot, regiontree.nodes[l].item.rx - t);
		regiontree.nodes[r].item.norm();
		regiontree.nodes[l].item.lineroot = mergefunc(regiontree.nodes[l].item.lineroot, regiontree.nodes[r].item.lineroot);
		regiontree.nodes[l].item.rx = regiontree.nodes[r].item.rx;
		r = regiontree.disconnect(r, 1);
	} else {
		regiontree.nodes[r].item.norm();
		regiontree.nodes[r].item.lineroot = lgrowfunc(regiontree.nodes[r].item.lineroot, regiontree.nodes[r].item.lx - t);
	}
	return regiontree.join(l, r);
}

int solve() {
	//REP(i, nrect) printf("t=%d..%d y=%d..%d to %d..%d\n", rect[i].lt, rect[i].rt, rect[i].lx - rect[i].lt, rect[i].rx - rect[i].lt, rect[i].lx - rect[i].rt, rect[i].rx - rect[i].rt);

	linetree.reset();
	regiontree.reset();
	int linedn = linetree.add(Line(-INF, sx, abs(-INF - sx), -1));
	int lineup = linetree.add(Line(sx, +INF, 0, +1));
	int lineroot = linetree.join(linedn, lineup);
	int regionroot = regiontree.add(Region(-INF, +INF, 0, lineroot, 0));

	vector<pair<int, int>> e;
	REP(i, nrect) e.PB(MP(2 * rect[i].lt + 1, i)), e.PB(MP(2 * rect[i].rt + 0, i));
	sort(e.begin(), e.end());
	//printf("INITIAL\n"); print(regionroot);
	REPSZ(i, e) {
		t = e[i].first >> 1; int kind = e[i].first & 1, idx = e[i].second;
		if (kind == 0) { // release rect
			int l, m, r;
			regiontree.split(regionroot, rect[idx].lx + 1, l, m);
			regiontree.split(m, rect[idx].rx, m, r);
			regiontree.apply(m, LazyRegion(-1));
			regionroot = regiontree.join(regiontree.join(l, m), r);
			regionroot = rgrow(regionroot, rect[idx].lx);
			regionroot = lgrow(regionroot, rect[idx].rx);
		}
		if (kind == 1) { // block rect
			int l, m, r;
			regiontree.split(regionroot, rect[idx].lx + 1, l, m);
			//printf("L\n"); print(l);
			//printf("M\n"); print(m);
			regiontree.split(m, rect[idx].rx, m, r);
			//printf("M\n"); print(m);
			//printf("R\n"); print(r);
			m = killzeroes(m);
			//printf("M\n"); print(m);
			regiontree.apply(m, LazyRegion(1));
			regionroot = regiontree.join(regiontree.join(l, m), r);
		}
		//printf("after %s rect %d (t=%d)\n", kind == 0 ? "releasing" : "blocking", idx + 1, t); print(regionroot);
		//if (i == 0) exit(0);
	}
	//printf("FINAL (t=%d)\n",t); print(regionroot);

	auto finalregions = regiontree.all(regionroot);
	assert(SZ(finalregions) == 1);
	auto finalregion = finalregions[0];
	finalregion.norm();
	assert(finalregion.lineroot != -1);
	auto finalfunc = linetree.all(finalregion.lineroot);
	int ret = INT_MAX;
	for (auto func : finalfunc) ret = min(ret, min(func.lcost, func.rcost()));
	return ret;
}

void run() {
	scanf("%d", &nrect);
	scanf("%d", &sx);
	REP(i, nrect) scanf("%d%d%d%d", &rect[i].lt, &rect[i].rt, &rect[i].lx, &rect[i].rx), --rect[i].lt, ++rect[i].rt, --rect[i].lx, ++rect[i].rx;
	printf("%d\n", solve());
}

void stress() {
	int mxrect = 100, mxdim = 100;
	REP(rep, 10000) {
		nrect = rnd() % mxrect + 1;
		int tdim = rnd() % mxdim + 1;
		int xdim = rnd() % mxdim + 1;
		sx = rnd() % (xdim + 1);
		REP(i, nrect) {
			rect[i].lt = rnd() % tdim; rect[i].rt = rnd() % tdim; if (rect[i].lt > rect[i].rt) swap(rect[i].lt, rect[i].rt); rect[i].rt += 2;
			rect[i].lx = rnd() % xdim; rect[i].rx = rnd() % xdim; if (rect[i].lx > rect[i].rx) swap(rect[i].lx, rect[i].rx); rect[i].rx += 2;
		}
		//printf("%d\n%d\n", nrect, sx); REP(i, nrect) printf("%d %d %d %d\n", rect[i].lt + 1, rect[i].rt - 1, rect[i].lx + 1, rect[i].rx - 1);
		solve();
		printf(".");
	}
}

int main() {
	run();
	//stress();
	return 0;
}

```