Codeforce 550 D Regular Bridge

Test instructions: Create a connected graph with a degree of K for all points and at least one bridge.

Practice: First build a bridge, and then on both sides of the bridge to establish two degrees K-connected graph, through the bridge to join together.

It is clear that K is even when there is no solution.

#include <map> #include <string> #include <cstring> #include <cstdio> #include <cstdlib># include<cmath> #include <queue> #include <vector> #include <iostream> #include <algorithm > #include <bitset> #include <climits> #include <list> #include <iomanip> #include <stack > #include <set>using namespace std;int main () {int n;cin>>n;if (n%2==0) {puts ("NO"); return 0;} Puts ("YES"), if (n==1) {printf ("2 1\n1 2"); return 0;} n++;cout<<2*n+2<< ""; if (n&1) cout<<n*n<<endl;elsecout<<n*n-1<<endl;for ( int i=1;i<=n;i++) {if (i<n-1) {cout<<i<< "" <<2*n+1<<endl;cout<<i+n<< "" <<2*n+2<<endl;} if (i==n-1) {cout<<i<< "" <<i+1<<endl;cout<<i+n<< "" &LT;&LT;I+1+N&LT;&LT;ENDL;} for (int j=i+1;j<=n;j++) {if (!) ( (i&1) &&j==i+1) {cout<<i<< "<<j<<endl;cout<<i+n<<" "<<j+n <<endl;}}}cout<<2*n+1<< "" <<2*n+2<<endl;} 

Time limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

An undirected graph was called K-regular, if the degrees of all their vertices is equal K. An edge of a connected graph was called a bridge, if after removing it the graph was being split into the other connected Components.

Build a connected undirected k-regular graph containing at least one bridge, or else state that such graph doesn ' T exist.

Input

The single line of the input contains integer k (1?≤? K.≤?100)-the required degree of the vertices of the regular graph.

Output

Print "NO" (without quotes), if such graph doesn ' t exist.

Otherwise, print "YES" in the first line and the description for any suitable graph in the next lines.

The description of the made graph must start with numbers n and m -the number of vertices and edges res Pectively.

Each of the nextmLines must contain, integers,aandb(1?≤? a,? b? ≤? N , a? ≠? b ), that's mean that there was an edge connecting the verticesaandb. A graph shouldn ' t contain multiple edges and edges that leads from a vertex to itself. A graph must is connected, the degrees of all vertices of the graph must be equalk. At least one edge of the graph must is a bridge. You can print the edges of the graph in any order. You can print the ends of each edge in any order.

The constructed graph must contain at mostTen6 Vertices andTen6 Edges (It is guaranteed so if at least one graph that meets the requirements exists and then there also exists the graph WI Th at mostTen6 Vertices and at the mostTen6 edges).

Sample Test (s) input

1

Output

YES2 11 2

Note

The sample from the statement there is a suitable graph consisting of the vertices, connected by a single edge.

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Codeforce 550 D Regular Bridge