Ivan has an array consisting of n different integers. He decided to reorder all elements in increasing order. Ivan loves merge sort so he decided to represent his array with one or several increasing sequences which he then plans to merge into one sorted array.

Ivan represent his array with increasing sequences with help of the following algorithm.

While there is at least one unused number in array Ivan repeats the following procedure:

  * iterate through array from the left to the right; 
  * Ivan only looks at unused numbers on current iteration; 
  * if current number is the first unused number on this iteration or this number is greater than previous unused number on current iteration, then Ivan marks the number as used and writes it down. 



For example, if Ivan's array looks like [1, 3, 2, 5, 4] then he will perform two iterations. On first iteration Ivan will use and write numbers [1, 3, 5], and on second one — [2, 4].

Write a program which helps Ivan and finds representation of the given array with one or several increasing sequences in accordance with algorithm described above.

Input

The first line contains a single integer n (1 ≤ n ≤ 2·105) — the number of elements in Ivan's array.

The second line contains a sequence consisting of distinct integers a1, a2, ..., an (1 ≤ ai ≤ 109) — Ivan's array.

Output

Print representation of the given array in the form of one or more increasing sequences in accordance with the algorithm described above. Each sequence must be printed on a new line.

Examples

Input

5
1 3 2 5 4


Output

1 3 5 
2 4 


Input

4
4 3 2 1


Output

4 
3 
2 
1 


Input

4
10 30 50 101


Output

10 30 50 101 
import java.util.*;
import java.io.*;
public class lp1{  

public static void main(String[] args){

int n = ni();
int a[] = ai(n);

TreeSet<Integer> ts = new TreeSet();
ArrayList<Integer> ar[] = new ArrayList[n];
HashMap<Integer,Integer> hm = new HashMap();

for(int i=0;i<n;i++)
   ar[i] = new ArrayList();


ar[0].add(a[0]); hm.put(a[0],0); ts.add(a[0]);
int is=0; 
 // System.out.println("sonu singh");
for(int i=1;i<n;i++)
{
   Integer x = ts.lower(a[i]); 
   if(x==null)
     {
           ar[++is].add(a[i]);
           hm.put(a[i],is);
           ts.add(a[i]);
      }
    else{
           int index = hm.get(x);
           ar[index].add(a[i]);
           ts.remove(x);
           ts.add(a[i]);
           hm.put(a[i],index);
    }
}
  // System.out.println("sonusaj singh");
 for(int i=0;i<=is;i++)
   {
       for(Integer j : ar[i])
         p(j+" ");
         pn("");
   }
   out.flush();
}
 
/*static class pair
	{
		int a,b;
		pair(){}
		pair(int c,int d){a=c;b=d;}
		@Override
		public int hashCode(){return (a+" "+b).hashCode();}
		@Override public boolean equals(Object c){if(a==((pair)c).a&&b==((pair)c).b)return true;return false;}
	} */
static int get(int index)
        {
                return (index&(-index));
        }
static void add(int bit[],int index,int val)
        {
             while(index<bit.length)
               {
                    bit[index] = bit[index]+val;
                    index = index + get(index);
               }
        }
static int get(int bit[],int index)
         {
               int sum=0;
               while(index>0)
                {
                    sum = sum+bit[index];
                    index = index-get(index);
                }
              return sum;
         }
static void add(long bit[],int index,long val)
        {
             while(index<bit.length)
               {
                    bit[index] = bit[index]+val;
                    index = index + get(index);
               }
        }
static long get(long bit[],int index)
         {
               long sum=0;
               while(index>0)
                {
                    sum = sum+bit[index];
                    index = index-get(index);
                }
              return sum;
         } 
static void compress(int a[])
         {      
                int n = a.length;
                Integer ar[] = new Integer[n];
                for(int i=0;i<n;i++)
                     ar[i] = a[i];
                Arrays.sort(ar);
                HashMap<Integer,Integer> hm = new HashMap();
                int st=1;
                for(int i=0;i<n;i++)
                    if(!hm.containsKey(ar[i]))
                        hm.put(ar[i],st++);
                for(int i=0;i<n;i++)
                   a[i] = hm.get(a[i]);
         }
static int find(int x,int p[]){ if(x==p[x]) return x; return p[x]=find(p[x],p) ;}
static void union(int x,int y,int p[]){ int xr=find(x,p),yr=find(y,p); if(xr!=yr){ p[xr]=yr;} }
 
static int abs(int x){ return x>0 ? x : -x; }
static long abs(long x){ return x>0 ? x : -x; }
static long gcd(long a,long b){ if(a==0)return b; if(b==0) return a;if(b%a==0) return a;return gcd(b%a,a); }
static int gcd(int a,int b){ if(a==0)return b; if(b==0) return a; if(b%a==0) return a;return gcd(b%a,a); }
static long min(long a,long b){ return a<b ? a : b; }
static int min(int a,int b){ return a<b ? a : b; }
static long max(long a,long b){ return a>b ? a : b; }
static int max(int a,int b){ return a>b ? a : b; }
static long pow(long a,long b,long md){ long ans=1;  while(b>0){if(b%2==1) ans = (ans*a)%md; a = (a*a)%md; b = b/2;} return ans; }
static int log2n(long a){ int te=0; while(a>0) {a>>=1; ++te; } return te; }

static void reverse(int a[]){int i1=0,i2=a.length-1; while(i1<i2){int t = a[i1];a[i1]=a[i2];a[i2]=t;i1++;i2--;}  } 
//static void reverse(long a[]){ int i1=0,i2=a.length-1; while(i1<i2){ long t = a[i1]; a[i1]=a[i2];a[i2]=t;i1++;i2--;}  } 

static void subtract_1(char s[]){if(s[0]=='0') return;int n = s.length,i=n-1;while(s[i]=='0')i--;s[i] =(char)((int)(s[i]-'0') + 47);for(int j=i+1;j<n;j++)s[j]='9';}
static void reverse(char s[]){int i1=0,i2=s.length-1; while(i1<i2){char t=s[i1];s[i1]=s[i2];s[i2]=t; i1++;i2--;} }
static String reverse(String r){String s = "";int i= r.length()-1; while(i>=0){ s=s+r.charAt(i);i--;}return s;}
static boolean pal(char s[]){ int i1=0,i2=s.length-1; while(i1<i2){ if(s[i1]!=s[i2]) return false; i1++;i2--;} return true;}
static boolean pal(String s){int n = s.length(),i1=0,i2=n-1;while(i1<i2){if(s.charAt(i1)!=s.charAt(i2))return false;i1++; i2--;}return true;}
 
// Input OutPut Functions
static PrintWriter out = new PrintWriter(System.out);
static FastReader sc=new FastReader();
static int ni(){ int x = sc.nextInt();return(x); }
static long nl(){ long x = sc.nextLong(); return(x); }
static String n(){ String str = sc.next(); return(str); }
static String ns(){ String str = sc.nextLine(); return(str);}
static double nd(){double d = sc.nextDouble(); return(d); }
static int[] ai(int n){ int a[] = new int[n]; for(int i=0;i<n;i++) a[i] = ni(); return a; }
static long[] al(int n) {long a[] = new long[n]; for(int i=0;i<n;i++) a[i] = nl(); return a; }
static double[] ad(int n) { double a[]= new double[n]; for(int i=0;i<n;i++) a[i]=nd(); return a;} 
static String[] as(int n){ String a[] = new String[n]; for(int i=0;i<n;i++) a[i] = n(); return a; }
static void p(Object o){ out.print(o); }
static void pn(Object o){ out.println(o); } 
 
static class FastReader{ 
BufferedReader br; 
StringTokenizer st;   
public FastReader() { br = new BufferedReader(new InputStreamReader(System.in));  }   
String next(){while(st==null || !st.hasMoreElements()){try{st = new StringTokenizer(br.readLine());}catch (IOException  e){e.printStackTrace();}}return st.nextToken();} 
int nextInt(){ return Integer.parseInt(next()); } 
long nextLong(){ return Long.parseLong(next()); } 
double nextDouble(){return Double.parseDouble(next()); } 
String nextLine(){ String str = ""; try{ str = br.readLine();} catch (IOException e){ e.printStackTrace();} return str;} 
  } 
}