Problem: Fillomino is a classic logic puzzle. (You do not need to know Fillomino in order to solve this problem.) In one classroom in Yunqi town, some volunteers are playing a board game variant of it:

Consider an n by n chessboard. Its rows are numbered from 1 to n from the top to the bottom. Its columns are numbered from 1 to n from the left to the right. A cell on an intersection of x-th row and y-th column is denoted (x, y). The main diagonal of the chessboard is cells (x, x) for all 1 ≤ x ≤ n.

A permutation of \{1, 2, 3, ..., n\} is written on the main diagonal of the chessboard. There is exactly one number written on each of the cells. The problem is to partition the cells under and on the main diagonal (there are exactly 1+2+ … +n such cells) into n connected regions satisfying the following constraints:

  1. Every region should be connected. That means that we can move from any cell of a region to any other cell of the same region visiting only cells of the same region and moving from a cell to an adjacent cell. 
  2. The x-th region should contain cell on the main diagonal with number x for all 1≤ x≤ n. 
  3. The number of cells that belong to the x-th region should be equal to x for all 1≤ x≤ n. 
  4. Each cell under and on the main diagonal should belong to exactly one region. 

Input

The first line contains a single integer n (1≤ n ≤ 500) denoting the size of the chessboard.

The second line contains n integers p_1, p_2, ..., p_n. p_i is the number written on cell (i, i). It is guaranteed that each integer from \{1, …, n\} appears exactly once in p_1, ..., p_n.

Output

If no solution exists, output -1.

Otherwise, output n lines. The i-th line should contain i numbers. The j-th number on the i-th line should be x if cell (i, j) belongs to the the region with x cells.

Examples

Input


3
2 3 1


Output


2
2 3
3 3 1


Input


5
1 2 3 4 5


Output


1
2 2
3 3 3
4 4 4 4
5 5 5 5 5

Note

The solutions to the examples are illustrated in the following pictures: <image> <image>

Solution (in JAVA):

Solution:
import java.math.*;
import java.util.*;
import java.io.*;



public class main
{
  static Map<String,Integer> map=new HashMap<>();
    public static void main(String[] args)
    {
        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
         final int mod=1000000007;
        int test_case =1;
                    StringBuilder sb=new StringBuilder();
      for(int t1=0;t1<test_case;t1++)
      {
          int n=in.nextInt();
          int[][] a=new int[n][n];
          
         for(int i=0;i<n;i++)
         {
             a[i][i]=in.nextInt();
         }
          
          for(int i=0;i<n;i++)
          {
              int temp=a[i][i]-1;
              int k=i;
              int j=i;
              while(true)
              {
                  if(temp==0)
                  {
                      break;
                  }else{
                      if(k>0&&a[j][k-1]==0)
                      {
                          k--;
                          a[j][k]=a[i][i];
                          temp--;
                      }else{
                          j++;
                          a[j][k]=a[i][i];
                          temp--;
                      }
                  }
              }
              
          }
          
          for(int i=0;i<n;i++)
          {
              for(int j=0;j<=i;j++)
              {
                  System.out.print(a[i][j]+" ");
              }
              System.out.println();
          }
          

              
          
      }
    
 
 
        pw.flush();
        pw.close();
    }
    
    
    static int factorial(int n,int mod)
    {
        long res = 1;
        for (int i=2; i<=n; i++)
            res=((res%mod)*(i%mod))%mod;
        return (int)res;
    }
    


    
    static int length(long l)
    {
        int c=0;
        while(l>0)
        {
            c++;
            l/=2;
        }
        
        return c;
    }

    
    static int CeilIndex(int A[], int l, int r, int key) 
    { 
        while (r - l > 1) { 
            int m = l + (r - l) / 2; 
            if (A[m] <= key) 
                r = m; 
            else
                l = m; 
        } 
  
        return r; 
    } 
    static int LongestIncreasingSubsequenceLength(int A[], int size) 
    { 
        // Add boundary case, when array size is one 
  
        int[] tailTable = new int[size]; 
        int len; // always points empty slot 
  
        tailTable[0] = A[0]; 
        len = 1; 
        for (int i = 1; i < size; i++) { 
            if (A[i] > tailTable[0]) 
 
                tailTable[0] = A[i]; 
  
            else if (A[i] <= tailTable[len - 1]) 
 
                tailTable[len++] = A[i]; 
  
            else
 
                tailTable[CeilIndex(tailTable, -1, len - 1, A[i])] = A[i]; 
        } 
  
        return len; 
    }
    
 
    
    static int[] next(int arr[], int n) { 
 
        Stack<Integer> S = new Stack<>(); 
  
        int[] next=new int[n];
 
        for (int i = n-1; i >= 0; i--) { 
 
            while (!S.empty() && arr[S.peek()] <= arr[i]) { 
                S.pop(); 
 
            } 
            if (S.empty()) { 
                next[i]=-1;
            } 
            else 
            { 
 
                next[i]=S.peek(); 
            } 
            S.push(i); 
        } 
        return next;
    }
    static int[] back(int arr[], int n) { 
 
        Stack<Integer> S = new Stack<>(); 
  
        int[] back=new int[n];
 
        for (int i = 0; i < n; i++) { 
 
            while (!S.empty() && arr[S.peek()] < arr[i]) { 
                S.pop(); 
            } 
            if (S.empty()) { 
                back[i]=-1;
            } 
            else 
            { 
                back[i]=S.peek(); 
            } 
            S.push(i); 
        } 
        
        return back;
    }
 
    
    
 
    static class InputReader
    {
 
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }
 
        public int snext()
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars)
            {
                curChar = 0;
                try
                {
                    snumChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n)
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt();
            }
            return a;
        }
        public long[] nextlongArray(int n)
        {
            long a[] = new long[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextLong();
            }
            return a;
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine()
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c)
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
 
    public static long mod = 1000000007;
    public static int d;
    public static int p;
    public static int q;
 
    public static int[] suffle(int[] a,Random gen)
    {
        int n = a.length;
        for(int i=0;i<n;i++)
        {
            int ind = gen.nextInt(n-i)+i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }
 
    public static void swap(int a, int b){
        int temp = a;
        a = b;
        b = temp;
    }
 
    public static HashSet<Integer> primeFactorization(int n)
    {
        HashSet<Integer> a =new HashSet<Integer>();
        for(int i=2;i*i<=n;i++)
        {
            while(n%i==0)
            {
                a.add(i);
                n/=i;
            }
        }
        if(n!=1)
            a.add(n);
        return a;
    }
 
    public static void sieve(boolean[] isPrime,int n)
    {
        for(int i=1;i<n;i++)
            isPrime[i] = true;
 
        isPrime[0] = false;
        isPrime[1] = false;
 
        for(int i=2;i*i<n;i++)
        {
            if(isPrime[i] == true)
            {
                for(int j=(2*i);j<n;j+=i)
                    isPrime[j] = false;
            }
        }
    }
 
    public static int GCD(int a,int b)
    {
        if(b==0)
            return a;
        else
            return GCD(b,a%b);
    }
 
    public static long GCD(long a,long b)
    {
        if(b==0)
            return a;
        else
            return GCD(b,a%b);
    }
 
    public static void extendedEuclid(int A,int B)
    {
        if(B==0)
        {
            d = A;
            p = 1 ;
            q = 0;
        }
        else
        {
            extendedEuclid(B, A%B);
            int temp = p;
            p = q;
            q = temp - (A/B)*q;
        }
    }
 
    public static long LCM(long a,long b)
    {
        return (a*b)/GCD(a,b);
    }
 
    public static int LCM(int a,int b)
    {
        return (a*b)/GCD(a,b);
    }
 
    public static int binaryExponentiation(int x,int n)
    {
        int result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=result * x;
            x=x*x;
            n=n/2;
        }
        return result;
    }
    int binarySearch(int arr[], int l, int r, int x) 
    { 
        if (r >= l) { 
            int mid = l + (r - l) / 2; 
  
 
            if (arr[mid] == x) 
                return mid; 
  
 
            if (arr[mid] > x) 
                return binarySearch(arr, l, mid - 1, x); 
  
 
            return binarySearch(arr, mid + 1, r, x); 
        } 
  
 
        return -1; 
    } 
  
 
    public static long binaryExponentiation(long x,long n)
    {
        long result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=result * x;
            x=x*x;
            n=n/2;
        }
        return result;
    }
 
    public static int modularExponentiation(int x,int n,int M)
    {
        int result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=(result * x)%M;
            x=(x*x)%M;
            n=n/2;
        }
        return result;
    }
 
    public static long modularExponentiation(long x,long n,long M)
    {
        long result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=(result * x)%M;
            x=(x*x)%M;
            n=n/2;
        }
        return result;
    }
 
    public static int modInverse(int A,int M)
    {
        return modularExponentiation(A,M-2,M);
    }
 
    public static long modInverse(long A,long M)
    {
        return modularExponentiation(A,M-2,M);
    }
 
    public static boolean isPrime(int n)
    {
 
        if (n <= 1)  return false;
        if (n <= 3)  return true;
 
        if (n%2 == 0 || n%3 == 0)
            return false;
 
        for (int i=5; i*i<=n; i=i+6)
        {
            if (n%i == 0 || n%(i+2) == 0)
                return false;
        }
 
        return true;
    }
    static class Pair
    {
        long  x;
        int  y;
    }
 
    static class pair implements Comparable<pair>
    {
        Integer x, y;
        pair(int x,int y)
        {
            this.x=x;
            this.y=y;
        }
 
        public int compareTo(pair o) {
            int result = x.compareTo(o.x);
            if(result==0)
                result = y.compareTo(o.y);
 
            return result;
        }
 
        public String toString()
        {
            return x+" "+y;
        }
 
        public boolean equals(Object o)
        {
            if (o instanceof pair)
            {
                pair p = (pair)o;
                return (Math.abs(p.x-x)==0 && Math.abs(p.y-y)==0);
            }
            return false;
        }
 
        public int hashCode()
        {
            return new Long(x).hashCode()*31 + new Long(y).hashCode();
        }
    }
}