import java.util.*;
import java.math.*;
import static java.lang.Math.*;public class AddElectricalWires {static class UnionSet {public int[] father=null;public int[] size=null;public int[] edges=null;public UnionSet(int n) {father=new int[n];size=new int[n];edges=new int[n];for(int i=0;i<n;++i) {father[i]=i;size[i]=1;}}public int getFather(int x) {if(father[x]==x) {return x;}return father[x]=getFather(father[x]);}public UnionSet merge(int x,int y) {int fx=getFather(x);int fy=getFather(y);if(fx!=fy) {father[fx]=fy;size[fy]+=size[fx];edges[fy]+=edges[fx]+1;}else {edges[fy]+=1;}return this;}}public int maxNewWires(String[] wires,int[] gridConnections) {final int n=wires.length;UnionSet unionSet=new UnionSet(n);for(int i=0;i<n;++i) {for(int j=i+1;j<n;++j) {if(wires[i].charAt(j)=='1') {unionSet.merge(i,j);}}}int result=0;long visited=0;int maxSize=0;for(int i=0;i<gridConnections.length;++i) {int t=gridConnections[i];int ft=unionSet.getFather(t);int sz=unionSet.size[ft];result+=sz*(sz-1)/2-unionSet.edges[ft];visited|=1l<<ft;if(sz>maxSize) {maxSize=sz;}}for(int i=0;i<n;++i) {if(i==unionSet.getFather(i)&&(0==(visited&(1l<<i)))) {int sz=unionSet.size[i];result+=sz*(sz-1)/2-unionSet.edges[i];result+=sz*maxSize;maxSize+=sz;}}return result;}
}

import java.util.*;
import java.math.*;
import static java.lang.Math.*;public class ContiguousCache {public long minimumReads(int n, int k, int[] addresses) {List<Integer> list=new ArrayList<>();final int m=addresses.length;for(int i=0;i<m;++i) {final int t=addresses[i];if(t-k+1>=0) {list.add(t-k+1);}if(t<=n-k) {list.add(t);}else {list.add(n-k);}}int[] a=unique(list);final int p=a.length;long[][] f=new long[m][p];for(int i=0;i<m;++i) {for(int j=0;j<p;++j) {f[i][j]=-1;}}for(int i=0;i<p;++i){if(a[i]<=addresses[0]&&addresses[0]<a[i]+k) {f[0][i]=Math.min(n,a[i]+k-1)-a[i]+1;}}for(int i=1;i<m;++i) {final int r=addresses[i];for(int j=0;j<p;++j) {if(f[i-1][j]==-1) {continue;}for(int t=0;t<p;++t) {if(a[t]<=r&&r<a[t]+k) {long cost=f[i-1][j]+calCost(a[j],a[t],k);if(f[i][t]==-1||f[i][t]>cost) {f[i][t]=cost;}}}}}long result=-1;for(int i=0;i<p;++i) {if(f[m-1][i]==-1) {continue;}if(result==-1||result>f[m-1][i]) {result=f[m-1][i];}}return result;}int calCost(int p1,int p2,int k) {if(p1<p2) {if(p1+k<=p2) {return k;}return p2-p1;}else if(p1==p2) {return 0;}else {if(p2+k<=p1) {return k;}return p1-p2;}}int[] unique(List<Integer> list) {Collections.sort(list);int c=1;int pre=0;for(int i=1;i<list.size();++i) {if(list.get(i)==list.get(pre)) {continue;}++c;pre=i;}int[] a=new int[c];a[0]=list.get(0);c=1;for(int i=1;i<list.size();++i) {if(a[c-1]!=list.get(i)) {a[c++]=list.get(i);}}return a;}
}

import java.util.*;
import java.math.*;
import static java.lang.Math.*;public class WifiPlanet {public long routersNeeded(int[] x, int[] y, int denom) {final int n=x.length;long result=0;for(int i=0;i<n;++i) {result+=cal(x[i],y[i],x[(i+1)%n],y[(i+1)%n],denom);}if(result<0) {result=-result;}return result;}long cal(long x1,long y1,long x2,long y2,long m) {if(x1==x2) {return 0;}if(x1>x2) {return -cal(x2,y2,x1,y1,m);}long L=(x1+m-1)/m*m;long R=(x2-1)/m*m;long n=(R-L)/m+1;return dfs((y1*(x2-x1)+(y2-y1)*(L-x1))/m,y2-y1,n,x2-x1);}long dfs(long a,long d,long n,long m) {if(n==0) {return 0;}if(d==0) {return a/m*n;}if(d<0) {return dfs(a+d*(n-1),-d,n,m);}if(a>=m) {return dfs(a%m,d,n,m)+a/m*n;}if(d>=m) {return dfs(a,d%m,n,m)+(d/m)*n*(n-1)/2;}return dfs((a+n*d)%m,m,(a+n*d)/m,d);}}