    #include <bits/stdc++.h>
                                                #include<iostream>
                                                #include<cstdio>
                                                #include<vector>
                                                #include<queue>
                                                #include<map>
                                                #include<cstring>
                                                #include<string>
                                                #include <math.h>
                                                #include<algorithm>
                                            //    #include <boost/multiprecision/cpp_int.hpp>
                                                #include<functional>
                                       #define int long long
                                                #define inf  1000000007
                                               #define pa pair<int,int>
                                         //       #define pa pair<double,double>
                                                #define ll long long
                                                #define pal pair<double,double>
                                                #define ppap pair<pa,int>
                                          #define PI 3.14159265358979323846
                                                #define paa pair<int,char>
                                                #define  mp make_pair
                                                #define  pb push_back
                                                #define EPS (1e-10)
                                                #define equals(a,b) (fabs((a)-(b))<EPS)
        int dx[4]={0,-1,0,1};
        int dy[4]={1,0,-1,0};
                                                using namespace std;
                                       			class pa3{
                                                	public:
                                                	int x,y,z;
                                                	pa3(int x=0,int y=0,int z=0):x(x),y(y),z(z) {}
                                                	bool operator < (const pa3 &p) const{
                                                		if(x!=p.x) return x<p.x;
                                                		if(y!=p.y) return y<p.y;
                                                		 return z<p.z;
                                                		//return x != p.x ? x<p.x: y<p.y;
                                                	}
                                       				bool operator > (const pa3 &p) const{
                                                		if(x!=p.x) return x>p.x;
                                                		if(y!=p.y) return y>p.y;
                                                		 return z>p.z;
                                                		//return x != p.x ? x<p.x: y<p.y;
                                                	}
                                                	bool operator == (const pa3 &p) const{
                                                		return x==p.x && y==p.y && z==p.z;
                                                	}
                                                		bool operator != (const pa3 &p) const{
                                                			return !( x==p.x && y==p.y && z==p.z);
                                                	}
                                                
                                                };
                                                
                                                class pa4{
                                                	public:
                                                	int x;
                                                	int y,z,w;
                                                	pa4(int x=0,int y=0,int z=0,int w=0):x(x),y(y),z(z),w(w) {}
                                                	bool operator < (const pa4 &p) const{
                                                		if(x!=p.x) return x<p.x;
                                                		if(y!=p.y) return y<p.y;
                                                		if(z!=p.z)return z<p.z;
                                                		return w<p.w;
                                                		//return x != p.x ? x<p.x: y<p.y;
                                                	}
                                                	bool operator > (const pa4 &p) const{
                                                		if(x!=p.x) return x>p.x;
                                                		if(y!=p.y) return y>p.y;
                                                		if(z!=p.z)return z>p.z;
                                                		return w>p.w;
                                                		//return x != p.x ? x<p.x: y<p.y;
                                                	}
                                                	bool operator == (const pa4 &p) const{
                                                		return x==p.x && y==p.y && z==p.z &&w==p.w;
                                                	}
                                                	
                                                	bool operator != (const pa4 &p) const{
                                                		return !(x==p.x && y==p.y && z==p.z &&w==p.w);
                                                	}
                                                		
                                                
                                                };
                                                class pa2{
                                                	public:
                                                	int x,y;
                                                	pa2(int x=0,int y=0):x(x),y(y) {}
                                                	pa2 operator + (pa2 p) {return pa2(x+p.x,y+p.y);}
                                                	pa2 operator - (pa2 p) {return pa2(x-p.x,y-p.y);}
                                                	bool operator < (const pa2 &p) const{
                                                		return x!= p.x ? x<p.x: y<p.y;
                                                	}
                                                	bool operator > (const pa2 &p) const{
                                                		return x != p.x ? x>p.x: y>p.y;
                                                	}
                                                	bool operator == (const pa2 &p) const{
                                                		return abs(x-p.x)==0 && abs(y-p.y)==0;
                                                	}
                                                	bool operator != (const pa2 &p) const{
                                                		return !(abs(x-p.x)==0 && abs(y-p.y)==0);
                                                	}
                                                		
                                                
                                                };
                                                
                                                       #define ppa pair<int,pas>
                                                class Point{
                                                	public:
                                                	double x,y;
                                                	Point(double x=0,double y=0):x(x),y(y) {}
                                                	Point operator + (Point p) {return Point(x+p.x,y+p.y);}
                                                	Point operator - (Point p) {return Point(x-p.x,y-p.y);}
                                                	Point operator * (double a) {return Point(x*a,y*a);}
                                                	Point operator / (double a) {return Point(x/a,y/a);}
                                                	double absv() {return sqrt(norm());}
                                                	double norm() {return x*x+y*y;}
                                                	bool operator < (const Point &p) const{
                                                		return x != p.x ? x<p.x: y<p.y;
                                                	}
                                                	bool operator == (const Point &p) const{
                                                		return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
                                                	}
                                                };
                                                typedef Point Vector;
                                         #define pl pair<int,pas>
                                                struct Segment{
                                                Point p1,p2;
                                                };
                                                 double dot(Vector a,Vector b){
                                                	return a.x*b.x+a.y*b.y;
                                                }
                                                double cross(Vector a,Vector b){
                                                	return a.x*b.y-a.y*b.x;
                                                }
                                            
                    bool parareru(Point a,Point b,Point c,Point d){
                    //	if(abs(cross(a-b,d-c))<EPS)cout<<"dd "<<cross(a-b,d-c)<<endl;
                    	return abs(cross(a-b,d-c))<EPS;
                    }
                    double distance_ls_p(Point a, Point b, Point c) {
                      if ( dot(b-a, c-a) < EPS ) return (c-a).absv();
                      if ( dot(a-b, c-b) < EPS ) return (c-b).absv();
                      return abs(cross(b-a, c-a)) / (b-a).absv();
                    }
                    bool is_intersected_ls(Segment a,Segment b) {
                    	if(a.p1==b.p1||a.p2==b.p1||a.p1==b.p2||a.p2==b.p2) return false;
                    	if(parareru((a.p2),(a.p1),(a.p1),(b.p2))&&parareru((a.p2),(a.p1),(a.p1),(b.p1))){
                    //		cout<<"sss"<<endl;
                    		if(dot(a.p1-b.p1,a.p1-b.p2)<EPS) return true;
                    		if(dot(a.p2-b.p1,a.p2-b.p2)<EPS) return true;
                    		if(dot(a.p1-b.p1,a.p2-b.p1)<EPS) return true;
                    		if(dot(a.p1-b.p2,a.p2-b.p2)<EPS) return true;
                    		return false;
                    	}
                      else return ( cross(a.p2-a.p1, b.p1-a.p1) * cross(a.p2-a.p1, b.p2-a.p1) < EPS ) && ( cross(b.p2-b.p1, a.p1-b.p1) * cross(b.p2-b.p1, a.p2-b.p1) < EPS );
                    }
                     
                    double segment_dis(Segment a,Segment b){
                    	if(is_intersected_ls(a,b))return 0;
                    	double r=distance_ls_p(a.p1, a.p2, b.p1);
                    	r=min(r,distance_ls_p(a.p1, a.p2, b.p2));
                    	r=min(r,distance_ls_p(b.p1, b.p2, a.p2));
                    	r=min(r,distance_ls_p(b.p1, b.p2, a.p1));
                    	return r;
                    }
                    Point intersection_ls(Segment a, Segment b) {
                      Point ba = b.p2-b.p1;
                      double d1 = abs(cross(ba, a.p1-b.p1));
                      double d2 = abs(cross(ba, a.p2-b.p1));
                      double t = d1 / (d1 + d2);
                     
                      return a.p1 + (a.p2-a.p1) * t;
                    }
                     
                                    string itos( int i ) {
                                    ostringstream s ;
                                    s << i ;
                                    return s.str() ;
                                    }
                                     
                                    int gcd(int v,int b){
                                    	if(v>b) return gcd(b,v);
                                    	if(v==b) return b;
                                    	if(b%v==0) return v;
                                    	return gcd(v,b%v);
                                    }
                     
                                    double distans(double x1,double y1,double x2,double y2){
                                    	double rr=(x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);
                                    	return sqrt(rr);
                                    	
                                    }
                                    int mod;
                    int pr[201000];
                    int inv[201000];
                   
                    int beki(int wa,int rr,int warukazu){
                    	if(rr==0) return 1%warukazu;
                    	if(rr==1) return wa%warukazu;
                    	if(rr%2==1) return (beki(wa,rr-1,warukazu)*wa)%warukazu;
                    	int zx=beki(wa,rr/2,warukazu);
                    	return (zx*zx)%warukazu;
                    }
                    /*
        double bekid(double w,int r){
        	if(r==0) return 1.0;
        	if(r==1) return w;
        	if(r%2) return bekid(w,r-1)*w;
        	double f=bekid(w,r/2);
        	return f*f;
        }*/
           /*       
        			int comb(int nn,int rr){
        				int r=pr[nn]*inv[rr];
        				r%=mod;
        				r*=inv[nn-rr];
        				r%=mod;
        				return r;
        			}
                  
                    void gya(int ert){
                    	pr[0]=1;
                    	for(int i=1;i<ert;i++){
                    		pr[i]=(pr[i-1]*i)%mod;
                    	}
                    	for(int i=0;i<ert;i++) inv[i]=beki(pr[i],mod-2,mod);
                    	
                    }
             */       
                  //   cin.tie(0);
        		//	ios::sync_with_stdio(false);
        			//priority_queue<pa3,vector<pa3>,greater<pa3>> pq;            
                     //sort(ve.begin(),ve.end(),greater<int>());
                                             //----------------kokomade tenpure------------

int iti[100020],ban[100020],a[100020],b[100020],ans[100020]={0};
  signed main(){
    	       cin.tie(0);
    			ios::sync_with_stdio(false);

int n,q;
  	cin>>n>>q;
  	iti[0]=1;
  	for(int i=1;i<=q;i++){
  	cin>>a[i]>>b[i];
  		if(iti[i-1]==a[i])iti[i]=b[i];
  		else if(iti[i-1]==b[i])iti[i]=a[i];
  		else iti[i]=iti[i-1];
  	}
  	for(int i=0;i<=n+1;i++)ban[i]=i;
  	
  	ans[iti[q]]=1;
   	ans[iti[q]-1]=1;
  	ans[iti[q]+1]=1;
  	
  	for(int i=q;i>0;i--){
  		swap(ban[a[i]],ban[b[i]]);
  		
  		ans[ban[iti[i-1]]]=1;
  		ans[ban[iti[i-1]+1]]=1;
  		ans[ban[iti[i-1]-1]]=1;
  	}
  	int g=0;
  	for(int i=1;i<=n;i++)if(ans[i])g++;
  	cout<<g<<endl;
        	return 0;
                }
### Prompt

Please provide a cpp coded solution to the problem described below:

You have N cups and 1 ball.

The cups are arranged in a row, from left to right.

You turned down all the cups, then inserted the ball into the leftmost cup.

Then, you will perform the following Q operations:

* The i-th operation: swap the positions of the A_i-th and B_i-th cups from the left. If one of these cups contains the ball, the ball will also move.



Since you are a magician, you can cast a magic described below:

* Magic: When the ball is contained in the i-th cup from the left, teleport the ball into the adjacent cup (that is, the (i-1)-th or (i+1)-th cup, if they exist).



The magic can be cast before the first operation, between two operations, or after the last operation, but you are allowed to cast it at most once during the whole process.

Find the number of cups with a possibility of containing the ball after all the operations and possibly casting the magic.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq Q \leq 10^5
* 1 \leq A_i < B_i \leq N

Input

The input is given from Standard Input in the following format:


N Q
A_1 B_1
A_2 B_2
:
A_Q B_Q


Output

Print the number of cups with a possibility of eventually containing the ball.

Examples

Input

10 3
1 3
2 4
4 5


Output

4


Input

20 3
1 7
8 20
1 19


Output

5

### Response

```cpp
    #include <bits/stdc++.h>
                                                #include<iostream>
                                                #include<cstdio>
                                                #include<vector>
                                                #include<queue>
                                                #include<map>
                                                #include<cstring>
                                                #include<string>
                                                #include <math.h>
                                                #include<algorithm>
                                            //    #include <boost/multiprecision/cpp_int.hpp>
                                                #include<functional>
                                       #define int long long
                                                #define inf  1000000007
                                               #define pa pair<int,int>
                                         //       #define pa pair<double,double>
                                                #define ll long long
                                                #define pal pair<double,double>
                                                #define ppap pair<pa,int>
                                          #define PI 3.14159265358979323846
                                                #define paa pair<int,char>
                                                #define  mp make_pair
                                                #define  pb push_back
                                                #define EPS (1e-10)
                                                #define equals(a,b) (fabs((a)-(b))<EPS)
        int dx[4]={0,-1,0,1};
        int dy[4]={1,0,-1,0};
                                                using namespace std;
                                       			class pa3{
                                                	public:
                                                	int x,y,z;
                                                	pa3(int x=0,int y=0,int z=0):x(x),y(y),z(z) {}
                                                	bool operator < (const pa3 &p) const{
                                                		if(x!=p.x) return x<p.x;
                                                		if(y!=p.y) return y<p.y;
                                                		 return z<p.z;
                                                		//return x != p.x ? x<p.x: y<p.y;
                                                	}
                                       				bool operator > (const pa3 &p) const{
                                                		if(x!=p.x) return x>p.x;
                                                		if(y!=p.y) return y>p.y;
                                                		 return z>p.z;
                                                		//return x != p.x ? x<p.x: y<p.y;
                                                	}
                                                	bool operator == (const pa3 &p) const{
                                                		return x==p.x && y==p.y && z==p.z;
                                                	}
                                                		bool operator != (const pa3 &p) const{
                                                			return !( x==p.x && y==p.y && z==p.z);
                                                	}
                                                
                                                };
                                                
                                                class pa4{
                                                	public:
                                                	int x;
                                                	int y,z,w;
                                                	pa4(int x=0,int y=0,int z=0,int w=0):x(x),y(y),z(z),w(w) {}
                                                	bool operator < (const pa4 &p) const{
                                                		if(x!=p.x) return x<p.x;
                                                		if(y!=p.y) return y<p.y;
                                                		if(z!=p.z)return z<p.z;
                                                		return w<p.w;
                                                		//return x != p.x ? x<p.x: y<p.y;
                                                	}
                                                	bool operator > (const pa4 &p) const{
                                                		if(x!=p.x) return x>p.x;
                                                		if(y!=p.y) return y>p.y;
                                                		if(z!=p.z)return z>p.z;
                                                		return w>p.w;
                                                		//return x != p.x ? x<p.x: y<p.y;
                                                	}
                                                	bool operator == (const pa4 &p) const{
                                                		return x==p.x && y==p.y && z==p.z &&w==p.w;
                                                	}
                                                	
                                                	bool operator != (const pa4 &p) const{
                                                		return !(x==p.x && y==p.y && z==p.z &&w==p.w);
                                                	}
                                                		
                                                
                                                };
                                                class pa2{
                                                	public:
                                                	int x,y;
                                                	pa2(int x=0,int y=0):x(x),y(y) {}
                                                	pa2 operator + (pa2 p) {return pa2(x+p.x,y+p.y);}
                                                	pa2 operator - (pa2 p) {return pa2(x-p.x,y-p.y);}
                                                	bool operator < (const pa2 &p) const{
                                                		return x!= p.x ? x<p.x: y<p.y;
                                                	}
                                                	bool operator > (const pa2 &p) const{
                                                		return x != p.x ? x>p.x: y>p.y;
                                                	}
                                                	bool operator == (const pa2 &p) const{
                                                		return abs(x-p.x)==0 && abs(y-p.y)==0;
                                                	}
                                                	bool operator != (const pa2 &p) const{
                                                		return !(abs(x-p.x)==0 && abs(y-p.y)==0);
                                                	}
                                                		
                                                
                                                };
                                                
                                                       #define ppa pair<int,pas>
                                                class Point{
                                                	public:
                                                	double x,y;
                                                	Point(double x=0,double y=0):x(x),y(y) {}
                                                	Point operator + (Point p) {return Point(x+p.x,y+p.y);}
                                                	Point operator - (Point p) {return Point(x-p.x,y-p.y);}
                                                	Point operator * (double a) {return Point(x*a,y*a);}
                                                	Point operator / (double a) {return Point(x/a,y/a);}
                                                	double absv() {return sqrt(norm());}
                                                	double norm() {return x*x+y*y;}
                                                	bool operator < (const Point &p) const{
                                                		return x != p.x ? x<p.x: y<p.y;
                                                	}
                                                	bool operator == (const Point &p) const{
                                                		return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
                                                	}
                                                };
                                                typedef Point Vector;
                                         #define pl pair<int,pas>
                                                struct Segment{
                                                Point p1,p2;
                                                };
                                                 double dot(Vector a,Vector b){
                                                	return a.x*b.x+a.y*b.y;
                                                }
                                                double cross(Vector a,Vector b){
                                                	return a.x*b.y-a.y*b.x;
                                                }
                                            
                    bool parareru(Point a,Point b,Point c,Point d){
                    //	if(abs(cross(a-b,d-c))<EPS)cout<<"dd "<<cross(a-b,d-c)<<endl;
                    	return abs(cross(a-b,d-c))<EPS;
                    }
                    double distance_ls_p(Point a, Point b, Point c) {
                      if ( dot(b-a, c-a) < EPS ) return (c-a).absv();
                      if ( dot(a-b, c-b) < EPS ) return (c-b).absv();
                      return abs(cross(b-a, c-a)) / (b-a).absv();
                    }
                    bool is_intersected_ls(Segment a,Segment b) {
                    	if(a.p1==b.p1||a.p2==b.p1||a.p1==b.p2||a.p2==b.p2) return false;
                    	if(parareru((a.p2),(a.p1),(a.p1),(b.p2))&&parareru((a.p2),(a.p1),(a.p1),(b.p1))){
                    //		cout<<"sss"<<endl;
                    		if(dot(a.p1-b.p1,a.p1-b.p2)<EPS) return true;
                    		if(dot(a.p2-b.p1,a.p2-b.p2)<EPS) return true;
                    		if(dot(a.p1-b.p1,a.p2-b.p1)<EPS) return true;
                    		if(dot(a.p1-b.p2,a.p2-b.p2)<EPS) return true;
                    		return false;
                    	}
                      else return ( cross(a.p2-a.p1, b.p1-a.p1) * cross(a.p2-a.p1, b.p2-a.p1) < EPS ) && ( cross(b.p2-b.p1, a.p1-b.p1) * cross(b.p2-b.p1, a.p2-b.p1) < EPS );
                    }
                     
                    double segment_dis(Segment a,Segment b){
                    	if(is_intersected_ls(a,b))return 0;
                    	double r=distance_ls_p(a.p1, a.p2, b.p1);
                    	r=min(r,distance_ls_p(a.p1, a.p2, b.p2));
                    	r=min(r,distance_ls_p(b.p1, b.p2, a.p2));
                    	r=min(r,distance_ls_p(b.p1, b.p2, a.p1));
                    	return r;
                    }
                    Point intersection_ls(Segment a, Segment b) {
                      Point ba = b.p2-b.p1;
                      double d1 = abs(cross(ba, a.p1-b.p1));
                      double d2 = abs(cross(ba, a.p2-b.p1));
                      double t = d1 / (d1 + d2);
                     
                      return a.p1 + (a.p2-a.p1) * t;
                    }
                     
                                    string itos( int i ) {
                                    ostringstream s ;
                                    s << i ;
                                    return s.str() ;
                                    }
                                     
                                    int gcd(int v,int b){
                                    	if(v>b) return gcd(b,v);
                                    	if(v==b) return b;
                                    	if(b%v==0) return v;
                                    	return gcd(v,b%v);
                                    }
                     
                                    double distans(double x1,double y1,double x2,double y2){
                                    	double rr=(x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);
                                    	return sqrt(rr);
                                    	
                                    }
                                    int mod;
                    int pr[201000];
                    int inv[201000];
                   
                    int beki(int wa,int rr,int warukazu){
                    	if(rr==0) return 1%warukazu;
                    	if(rr==1) return wa%warukazu;
                    	if(rr%2==1) return (beki(wa,rr-1,warukazu)*wa)%warukazu;
                    	int zx=beki(wa,rr/2,warukazu);
                    	return (zx*zx)%warukazu;
                    }
                    /*
        double bekid(double w,int r){
        	if(r==0) return 1.0;
        	if(r==1) return w;
        	if(r%2) return bekid(w,r-1)*w;
        	double f=bekid(w,r/2);
        	return f*f;
        }*/
           /*       
        			int comb(int nn,int rr){
        				int r=pr[nn]*inv[rr];
        				r%=mod;
        				r*=inv[nn-rr];
        				r%=mod;
        				return r;
        			}
                  
                    void gya(int ert){
                    	pr[0]=1;
                    	for(int i=1;i<ert;i++){
                    		pr[i]=(pr[i-1]*i)%mod;
                    	}
                    	for(int i=0;i<ert;i++) inv[i]=beki(pr[i],mod-2,mod);
                    	
                    }
             */       
                  //   cin.tie(0);
        		//	ios::sync_with_stdio(false);
        			//priority_queue<pa3,vector<pa3>,greater<pa3>> pq;            
                     //sort(ve.begin(),ve.end(),greater<int>());
                                             //----------------kokomade tenpure------------

int iti[100020],ban[100020],a[100020],b[100020],ans[100020]={0};
  signed main(){
    	       cin.tie(0);
    			ios::sync_with_stdio(false);

int n,q;
  	cin>>n>>q;
  	iti[0]=1;
  	for(int i=1;i<=q;i++){
  	cin>>a[i]>>b[i];
  		if(iti[i-1]==a[i])iti[i]=b[i];
  		else if(iti[i-1]==b[i])iti[i]=a[i];
  		else iti[i]=iti[i-1];
  	}
  	for(int i=0;i<=n+1;i++)ban[i]=i;
  	
  	ans[iti[q]]=1;
   	ans[iti[q]-1]=1;
  	ans[iti[q]+1]=1;
  	
  	for(int i=q;i>0;i--){
  		swap(ban[a[i]],ban[b[i]]);
  		
  		ans[ban[iti[i-1]]]=1;
  		ans[ban[iti[i-1]+1]]=1;
  		ans[ban[iti[i-1]-1]]=1;
  	}
  	int g=0;
  	for(int i=1;i<=n;i++)if(ans[i])g++;
  	cout<<g<<endl;
        	return 0;
                }
```