Problem: You are given an array of n elements, you must make it a co-prime array in as few moves as possible.

In each move you can insert any positive integral number you want not greater than 109 in any place in the array.

An array is co-prime if any two adjacent numbers of it are co-prime.

In the number theory, two integers a and b are said to be co-prime if the only positive integer that divides both of them is 1.

Input

The first line contains integer n (1 ≤ n ≤ 1000) — the number of elements in the given array.

The second line contains n integers ai (1 ≤ ai ≤ 109) — the elements of the array a.

Output

Print integer k on the first line — the least number of elements needed to add to the array a to make it co-prime.

The second line should contain n + k integers aj — the elements of the array a after adding k elements to it. Note that the new array should be co-prime, so any two adjacent values should be co-prime. Also the new array should be got from the original array a by adding k elements to it.

If there are multiple answers you can print any one of them.

Example

Input

3
2 7 28


Output

1
2 7 9 28

Solution (in JAVA):

Solution:
import java.io.File;import java.io.FileInputStream;import java.io.FileNotFoundException;
import java.io.IOException;import java.io.InputStream;import java.io.PrintWriter;
import java.lang.annotation.Retention;import java.lang.annotation.RetentionPolicy;
import java.lang.reflect.Array;import java.lang.reflect.Field;import java.lang.reflect.InvocationTargetException;
import java.lang.reflect.Method;import java.security.AccessControlException;import java.util.ArrayList;
import java.util.Arrays;import java.util.Collection;import java.util.Comparator;
import java.util.List;import java.util.Map;import java.util.Objects;import java.util.TreeMap;
import java.util.function.Function;import java.util.stream.Collectors;import java.util.stream.IntStream;
import java.util.stream.LongStream;import java.util.stream.Stream;public class _p000660A {
static public void main(final String[] args) throws IOException{p000660A._main(args);}

static class p000660A extends Solver{public p000660A(){singleTest=true;}@Override public 
void solve()throws IOException{int n=sc.nextInt();sc.nextLine();int[]a=Arrays.stream(sc.nextLine().trim().split("\\s+")).filter($s2
->!$s2.isEmpty()).mapToInt(Integer::parseInt).toArray();ArrayList<Integer>res=new 
ArrayList<>();res.add(a[0]);for(int i=1;i<n;i++){int left=res.get(res.size()-1);
int g=GreatestCommonFactor.apply(left,a[i]);if(g>1){int c=left/g;while(true){if(c
>1){int g1=GreatestCommonFactor.apply(left,c);int g2=GreatestCommonFactor.apply(c,
a[i]);if(g1==1 && g2==1){break;}}c++;}res.add(c);}res.add(a[i]);}pw.println(res.size()
-n);pw.println(Datas.join(res));}static public void _main(String[]args)throws IOException
{new p000660A().run();}}static class Datas{static class Pair<K,V>{private K k;private 
V v;public Pair(final K t,final V u){this.k=t;this.v=u;}public K getKey(){return 
k;}public V getValue(){return v;}}final static String SPACE=" ";public static TreeMap<Integer,
Integer>mapc(final int[]a){return IntStream.range(0,a.length).collect(()->new TreeMap<Integer,
Integer>(),(res,i)->{res.put(a[i],res.getOrDefault(a[i],0)+1);},Map::putAll);}public 
static TreeMap<Long,Integer>mapc(final long[]a){return IntStream.range(0,a.length).collect(
()->new TreeMap<Long,Integer>(),(res,i)->{res.put(a[i],res.getOrDefault(a[i],0)+
1);},Map::putAll);}public static<T>TreeMap<T,Integer>mapc(final T[]a,Comparator<T>
cmp){return IntStream.range(0,a.length).collect(cmp!=null?()->new TreeMap<T,Integer>(cmp)
:()->new TreeMap<T,Integer>(),(res,i)->{res.put(a[i],res.getOrDefault(a[i],0)+1);
},Map::putAll);}public static<T>TreeMap<T,Integer>mapc(final T[]a){return mapc(a,
null);}public static TreeMap<Integer,Integer>mapc(final IntStream a){return a.collect(
()->new TreeMap<Integer,Integer>(),(res,v)->{res.put(v,res.getOrDefault(v,0)+1);
},Map::putAll);}public static TreeMap<Long,Integer>mapc(final LongStream a){return 
a.collect(()->new TreeMap<Long,Integer>(),(res,v)->{res.put(v,res.getOrDefault(v,
0)+1);},Map::putAll);}public static<T>TreeMap<T,Integer>mapc(final Stream<T>a,Comparator<T>
cmp){return a.collect(cmp!=null?()->new TreeMap<T,Integer>(cmp):()->new TreeMap<T,
Integer>(),(res,v)->{res.put(v,res.getOrDefault(v,0)+1);},Map::putAll);}public static
<T>TreeMap<T,Integer>mapc(final Stream<T>a){return mapc(a,null);}public static<T>
TreeMap<T,Integer>mapc(final Collection<T>a,Comparator<T>cmp){return mapc(a.stream(),
cmp);}public static<T>TreeMap<T,Integer>mapc(final Collection<T>a){return mapc(a.stream());
}public static TreeMap<Integer,List<Integer>>mapi(final int[]a){return IntStream.range(0,
a.length).collect(()->new TreeMap<Integer,List<Integer>>(),(res,i)->{if(!res.containsKey(a[i]))
{res.put(a[i],Stream.of(i).collect(Collectors.toList()));}else{res.get(a[i]).add(i);
}},Map::putAll);}public static TreeMap<Long,List<Integer>>mapi(final long[]a){return 
IntStream.range(0,a.length).collect(()->new TreeMap<Long,List<Integer>>(),(res,i)
->{if(!res.containsKey(a[i])){res.put(a[i],Stream.of(i).collect(Collectors.toList()));
}else{res.get(a[i]).add(i);}},Map::putAll);}public static<T>TreeMap<T,List<Integer>>
mapi(final T[]a,Comparator<T>cmp){return IntStream.range(0,a.length).collect(cmp
!=null?()->new TreeMap<T,List<Integer>>(cmp):()->new TreeMap<T,List<Integer>>(),
(res,i)->{if(!res.containsKey(a[i])){res.put(a[i],Stream.of(i).collect(Collectors.toList()));
}else{res.get(a[i]).add(i);}},Map::putAll);}public static<T>TreeMap<T,List<Integer>>
mapi(final T[]a){return mapi(a,null);}public static TreeMap<Integer,List<Integer>>
mapi(final IntStream a){int[]i=new int[]{0};return a.collect(()->new TreeMap<Integer,
List<Integer>>(),(res,v)->{if(!res.containsKey(v)){res.put(v,Stream.of(i[0]).collect(Collectors.toList()));
}else{res.get(v).add(i[0]);}i[0]++;},Map::putAll);}public static TreeMap<Long,List<Integer>>
mapi(final LongStream a){int[]i=new int[]{0};return a.collect(()->new TreeMap<Long,
List<Integer>>(),(res,v)->{if(!res.containsKey(v)){res.put(v,Stream.of(i[0]).collect(Collectors.toList()));
}else{res.get(v).add(i[0]);}i[0]++;},Map::putAll);}public static<T>TreeMap<T,List<Integer>>
mapi(final Stream<T>a,Comparator<T>cmp){int[]i=new int[]{0};return a.collect(cmp
!=null?()->new TreeMap<T,List<Integer>>(cmp):()->new TreeMap<T,List<Integer>>(),
(res,v)->{if(!res.containsKey(v)){res.put(v,Stream.of(i[0]).collect(Collectors.toList()));
}else{res.get(v).add(i[0]);}i[0]++;},Map::putAll);}public static<T>TreeMap<T,List<Integer>>
mapi(final Stream<T>a){return mapi(a,null);}public static<T>TreeMap<T,List<Integer>>
mapi(final Collection<T>a,Comparator<T>cmp){return mapi(a.stream(),cmp);}public 
static<T>TreeMap<T,List<Integer>>mapi(final Collection<T>a){return mapi(a.stream());
}public static List<int[]>listi(final int[]a){return IntStream.range(0,a.length).mapToObj(i
->new int[]{a[i],i}).collect(Collectors.toList());}public static List<long[]>listi(final 
long[]a){return IntStream.range(0,a.length).mapToObj(i->new long[]{a[i],i}).collect(Collectors.toList());
}public static<T>List<Pair<T,Integer>>listi(final T[]a){return IntStream.range(0,
a.length).mapToObj(i->new Pair<T,Integer>(a[i],i)).collect(Collectors.toList());
}public static List<int[]>listi(final IntStream a){int[]i=new int[]{0};return a.mapToObj(v
->new int[]{v,i[0]++}).collect(Collectors.toList());}public static List<long[]>listi(final 
LongStream a){int[]i=new int[]{0};return a.mapToObj(v->new long[]{v,i[0]++}).collect(Collectors.toList());
}public static<T>List<Pair<T,Integer>>listi(final Stream<T>a){int[]i=new int[]{0};
return a.map(v->new Pair<T,Integer>(v,i[0]++)).collect(Collectors.toList());}public 
static<T>List<Pair<T,Integer>>listi(final Collection<T>a){int[]i=new int[]{0};return 
a.stream().map(v->new Pair<T,Integer>(v,i[0]++)).collect(Collectors.toList());}public 
static String join(final int[]a){return Arrays.stream(a).mapToObj(Integer::toString).collect(Collectors.joining(SPACE));
}public static String join(final long[]a){return Arrays.stream(a).mapToObj(Long::toString).collect(Collectors.joining(SPACE));
}public static<T>String join(final T[]a){return Arrays.stream(a).map(v->Objects.toString(v)).collect(Collectors.joining(SPACE));
}public static<T>String join(final T[]a,final Function<T,String>toString){return 
Arrays.stream(a).map(v->toString.apply(v)).collect(Collectors.joining(SPACE));}public 
static<T>String join(final Collection<T>a){return a.stream().map(v->Objects.toString(v)).collect(Collectors.joining(SPACE));
}public static<T>String join(final Collection<T>a,final Function<T,String>toString)
{return a.stream().map(v->toString.apply(v)).collect(Collectors.joining(SPACE));
}public static<T>String join(final Stream<T>a){return a.map(v->Objects.toString(v)).collect(Collectors.joining(SPACE));
}public static<T>String join(final Stream<T>a,final Function<T,String>toString){
return a.map(v->toString.apply(v)).collect(Collectors.joining(SPACE));}public static
<T>String join(final IntStream a){return a.mapToObj(Integer::toString).collect(Collectors.joining(SPACE));
}public static<T>String join(final LongStream a){return a.mapToObj(Long::toString).collect(Collectors.joining(SPACE));
}public static List<Integer>list(final int[]a){return Arrays.stream(a).mapToObj(Integer::valueOf).collect(Collectors.toList());
}public static List<Integer>list(final IntStream a){return a.mapToObj(Integer::valueOf).collect(Collectors.toList());
}public static List<Long>list(final long[]a){return Arrays.stream(a).mapToObj(Long::valueOf).collect(Collectors.toList());
}public static List<Long>list(final LongStream a){return a.mapToObj(Long::valueOf).collect(Collectors.toList());
}public static<T>List<T>list(final Stream<T>a){return a.collect(Collectors.toList());
}public static<T>List<T>list(final Collection<T>a){return a.stream().collect(Collectors.toList());
}public static<T>List<T>list(final T[]a){return Arrays.stream(a).collect(Collectors.toList());
}public static String yesNo(final boolean res){return res?"YES":"NO";}public static 
String dump(Object obj){String res="";if(obj!=null){Class cl=obj.getClass();String 
cls=cl.getName();if(cls.startsWith("[")){res+="[";for(int i=0;;i++){try{Object o
=Array.get(obj,i);String s=dump(o);if(i>0){res+=", ";}res+=s;}catch(ArrayIndexOutOfBoundsException 
ex){break;}}res+="]";}else if(Collection.class.isAssignableFrom(cl)){@SuppressWarnings("unchecked")final 
Object s=((Collection)obj).stream().map(v->dump(v)).collect(Collectors.joining(", ",
"[","]"));res+=s.toString();}else if(Map.class.isAssignableFrom(cl)){@SuppressWarnings("unchecked")final 
Object s=((Map)obj).entrySet().stream().map(v->dump(v)).collect(Collectors.joining(", ",
"{","}"));res+=s.toString();}else if(Character.class.isInstance(obj)|| Integer.class.isInstance(obj)
|| Long.class.isInstance(obj)|| Float.class.isInstance(obj)|| Double.class.isInstance(obj)|| String.class.isInstance(obj)
){res+=Objects.toString(obj);}else if(Map.Entry.class.isInstance(obj)){res+=dump(((Map.Entry)obj).getKey())
+"="+dump(((Map.Entry)obj).getValue());}else if(Stream.class.isInstance(obj)){@SuppressWarnings("unchecked")
final Object s=((Stream)obj).map(v->dump(v)).collect(Collectors.joining(", ","[",
"]"));res+=s.toString();}else{res+=Stream.concat(Arrays.stream(obj.getClass().getFields()).map(v
->{String name=v.getName();String val;try{Object o=v.get(obj);if(o!=null && v.isAnnotationPresent(Dump.class))
{Dump an=v.getAnnotation(Dump.class);Class ocl=o.getClass();val="{";for(String fn:an.fields())
{try{Field f=ocl.getField(fn);val+=fn+"="+dump(f.get(o))+", ";}catch(NoSuchFieldException 
nsfex){try{@SuppressWarnings("unchecked")final Method m=ocl.getMethod(fn);val+=fn+"="+dump(m.invoke(o))
+", ";}catch(NoSuchMethodException | IllegalArgumentException | InvocationTargetException 
nsmex){}}}if(val.endsWith(", ")){val=val.substring(0,val.length()-2);}val+="}";}
else{val=dump(o);}}catch(IllegalAccessException ex){val="N/A";}return name+"="+val;
}),Arrays.stream(obj.getClass().getMethods()).filter(m->m.isAnnotationPresent(Getter.class)).map(m
->{String name=m.getName();String val;try{Object o=m.invoke(obj);if(o!=null && m.isAnnotationPresent(Dump.class))
{Dump an=m.getAnnotation(Dump.class);Class ocl=o.getClass();val="{";for(String fn:an.fields())
{try{Field f=ocl.getField(fn);val+=fn+"="+dump(f.get(o))+", ";}catch(NoSuchFieldException 
nsfex){try{@SuppressWarnings("unchecked")final Method m1=ocl.getMethod(fn);val+=fn+"="+dump(m1.invoke(o))
+", ";}catch(NoSuchMethodException | IllegalArgumentException | InvocationTargetException 
nsmex){}}}if(val.endsWith(", ")){val=val.substring(0,val.length()-2);}val+="}";}else
{val=dump(o);}}catch(IllegalAccessException | InvocationTargetException ex){val=
"N/A";}return name+"="+val;})).collect(Collectors.joining(", ","{"+obj.getClass().getName()
+": ","}"));}}if(res.length()==0){res="<null>";}return res;}}@Retention(RetentionPolicy.RUNTIME)
public @interface Dump{String[]fields();}@Retention(RetentionPolicy.RUNTIME)public @interface Getter{}static class 
GreatestCommonFactor{public static int apply(int a,int b){int max=Math.max(a,b);
int min=Math.min(a,b);while(min>1){int r=max%min;if(r==0){return min;}max=min;min
=r;}return 1;}public static long apply(long a,long b){long max=Math.max(a,b);long 
min=Math.min(a,b);while(min>1){long r=max%min;if(r==0){return min;}max=min;min=r;
}return 1;}}static class MyScanner{private StringBuilder cache=new StringBuilder();
int cache_pos=0;private int first_linebreak=-1;private int second_linebreak=-1;private 
StringBuilder sb=new StringBuilder();private InputStream is=null;public MyScanner(final 
InputStream is){this.is=is;}public String charToString(final int c){return String.format("'%s'",
c=='\n'?"\\n":(c=='\r'?"\\r":String.valueOf((char)c)));}public int get(){int res
=-1;if(cache_pos<cache.length()){res=cache.charAt(cache_pos);cache_pos++;if(cache_pos
==cache.length()){cache.delete(0,cache_pos);cache_pos=0;}}else{try{res=is.read();
}catch(IOException ex){throw new RuntimeException(ex);}}return res;}private void 
unget(final int c){if(cache_pos==0){cache.insert(0,(char)c);}else{cache_pos--;}}
public String nextLine(){sb.delete(0,sb.length());int c;boolean done=false;boolean 
end=false;while((c=get())!=-1){if(check_linebreak(c)){done=true;if(c==first_linebreak)
{if(!end){end=true;}else{cache.append((char)c);break;}}else if(second_linebreak!=
-1 && c==second_linebreak){break;}}if(end && c!=first_linebreak && c!=second_linebreak)
{cache.append((char)c);break;}if(!done){sb.append((char)c);}}return sb.toString();
}private boolean check_linebreak(int c){if(c=='\n'|| c=='\r'){if(first_linebreak
==-1){first_linebreak=c;}else if(c!=first_linebreak && second_linebreak==-1){second_linebreak
=c;}return true;}return false;}public int nextInt(){return Integer.parseInt(next());
}public long nextLong(){return Long.parseLong(next());}public boolean hasNext(){
boolean res=false;int c;while((c=get())!=-1){if(!check_linebreak(c)&& c!=' '&& c
!='\t'){res=true;unget(c);break;}}return res;}public String next(){sb.delete(0,sb.length());
boolean started=false;int c;while((c=get())!=-1){if(check_linebreak(c)|| c==' '|| 
c=='\t'){if(started){unget(c);break;}}else{started=true;sb.append((char)c);}}return 
sb.toString();}public int nextChar(){return get();}public boolean eof(){int c=get();
boolean res=false;if(c!=-1){unget(c);}else{res=true;}return res;}public double nextDouble()
{return Double.parseDouble(next());}}static abstract class Solver{protected String 
nameIn=null;protected String nameOut=null;protected boolean singleTest=false;protected 
MyScanner sc=null;protected PrintWriter pw=null;private int current_test=0;private 
int count_tests=0;protected int currentTest(){return current_test;}protected int 
countTests(){return count_tests;}private void process()throws IOException{if(!singleTest)
{count_tests=sc.nextInt();sc.nextLine();for(current_test=1;current_test<=count_tests;
current_test++){solve();pw.flush();}}else{count_tests=1;current_test=1;solve();}
}abstract protected void solve()throws IOException;public void run()throws IOException
{boolean done=false;try{if(nameIn!=null){if(new File(nameIn).exists()){try(FileInputStream 
fis=new FileInputStream(nameIn);PrintWriter pw0=select_output();){select_output();
done=true;sc=new MyScanner(fis);pw=pw0;process();}}else{throw new RuntimeException("File "
+new File(nameIn).getAbsolutePath()+" does not exist!");}}}catch(IOException | AccessControlException 
ex){}if(!done){try(PrintWriter pw0=select_output();){sc=new MyScanner(System.in);
pw=pw0;process();}}}private PrintWriter select_output()throws FileNotFoundException
{if(nameOut!=null){return new PrintWriter(nameOut);}return new PrintWriter(System.out);
}}static abstract class Tester{static public int getRandomInt(final int min,final 
int max){return(min+(int)Math.floor(Math.random()*(max-min+1)));}static public long 
getRandomLong(final long min,final long max){return(min+(long)Math.floor(Math.random()
*(max-min+1)));}static public double getRandomDouble(final double min,final double 
maxExclusive){return(min+Math.random()*(maxExclusive-min));}abstract protected void 
testOutput(final List<String>output_data);abstract protected void generateInput();
abstract protected String inputDataToString();private boolean break_tester=false;
protected void beforeTesting(){}protected void breakTester(){break_tester=true;}
public boolean broken(){return break_tester;}}}