There is a white sheet of paper lying on a rectangle table. The sheet is a rectangle with its sides parallel to the sides of the table. If you will take a look from above and assume that the bottom left corner of the table has coordinates (0, 0), and coordinate axes are left and bottom sides of the table, then the bottom left corner of the white sheet has coordinates (x_1, y_1), and the top right — (x_2, y_2).

After that two black sheets of paper are placed on the table. Sides of both black sheets are also parallel to the sides of the table. Coordinates of the bottom left corner of the first black sheet are (x_3, y_3), and the top right — (x_4, y_4). Coordinates of the bottom left corner of the second black sheet are (x_5, y_5), and the top right — (x_6, y_6). 

<image> Example of three rectangles.

Determine if some part of the white sheet can be seen from the above after the two black sheets are placed. The part of the white sheet can be seen if there is at least one point lying not strictly inside the white sheet and strictly outside of both black sheets.

Input

The first line of the input contains four integers x_1, y_1, x_2, y_2 (0 ≤ x_1 < x_2 ≤ 10^{6}, 0 ≤ y_1 < y_2 ≤ 10^{6}) — coordinates of the bottom left and the top right corners of the white sheet.

The second line of the input contains four integers x_3, y_3, x_4, y_4 (0 ≤ x_3 < x_4 ≤ 10^{6}, 0 ≤ y_3 < y_4 ≤ 10^{6}) — coordinates of the bottom left and the top right corners of the first black sheet.

The third line of the input contains four integers x_5, y_5, x_6, y_6 (0 ≤ x_5 < x_6 ≤ 10^{6}, 0 ≤ y_5 < y_6 ≤ 10^{6}) — coordinates of the bottom left and the top right corners of the second black sheet.

The sides of each sheet of paper are parallel (perpendicular) to the coordinate axes.

Output

If some part of the white sheet can be seen from the above after the two black sheets are placed, print "YES" (without quotes). Otherwise print "NO".

Examples

Input


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


Output


NO


Input


3 3 7 5
0 0 4 6
0 0 7 4


Output


YES


Input


5 2 10 5
3 1 7 6
8 1 11 7


Output


YES


Input


0 0 1000000 1000000
0 0 499999 1000000
500000 0 1000000 1000000


Output


YES

Note

In the first example the white sheet is fully covered by black sheets.

In the second example the part of the white sheet can be seen after two black sheets are placed. For example, the point (6.5, 4.5) lies not strictly inside the white sheet and lies strictly outside of both black sheets.
    import java.io.BufferedWriter;
    import java.io.IOException;
    import java.io.InputStream;
    import java.io.OutputStream;
    import java.io.OutputStreamWriter;
    import java.io.PrintWriter;
    import java.io.Writer;
    import java.util.Arrays;
    import java.util.InputMismatchException;
    import java.util.*;
    import java.io.*;
    import java.math.*;
    public class Main6{
     
    static class Pair
    	{ 
    		int x;
    		int y;
    		int z;
    		public Pair(int x,int y,int z) 
    		{	 
    			this.x= x; 
    			this.y= y;
    			this.z=z;
    		}	 
    		
    	@Override
    			public int hashCode() 
    			{ 
    				final int temp = 14; 
    				int ans = 1; 
    				ans =x*31+y*13; 
    				return ans; 
    			} 
    	  
    			// Equal objects must produce the same 
    			// hash code as long as they are equal 
    		@Override
    		public boolean equals(Object o) 
    		{ 
    			if (this == o) { 
    				return true; 
    			} 
    			if (o == null) { 
    				return false; 
    			} 
    			if (this.getClass() != o.getClass()) { 
    				return false; 
    			} 
    			Pair other = (Pair)o; 
    			if (this.x != other.x || this.y!=other.y) { 
    				return false; 
    			} 
    			return true; 
    		} 
    			
    	} 
    	static class Pair1
    	{
    		String x;
    		int y;
    		int z;
    		
    	}
    	static class Compare
    	{ 
    		static void compare(Pair arr[], int n) 
    		{ 
    			// Comparator to sort the pair according to second element 
    		/*	Arrays.sort(arr, new Comparator<Pair>() { 
    				@Override public int compare(Pair p1, Pair p2) 
    				{ 
    					if(p1.start>p2.start)
    					{
    						return 1;
    					}
    					else if(p1.start==p2.start)
    					{
    						return 0;
    					}
    					else
    					{
    						return -1;
    					}
    				} 
    			}); */
    		}
    		
    	}
    	
    	
    	public static long pow(long a, long b)
    	{
    		long result=1;
    		while(b>0)
    		{
    			if (b % 2 != 0)
    			{
    				result=(result*a)%998244353;
    				b--;
    			} 
    			a=(a*a)%998244353;
    			b /= 2;
    		}   
    		return result;
    	}
    	public static long fact(long num)
    	{
    				long value=1;
    				int i=0;
    				for(i=2;i<num;i++)
    				{
    					value=((value%mod)*i%mod)%mod;
    				}
    				return value;
    			}
    			public static long gcd(long a, long b)
    			{
    				if (a == 0)
    					return b;
    				return gcd(b%a, a);
    			}
    			
    	/*		public static long lcm(long a,long b)
    			{
    				return a * (b / gcd(a, b));
    			}
    		*/	public static long sum(int h)
    			{
    				return (h*(h+1)/2);
    			}
    			public static void dfs(int parent,boolean[] visited,int[] dp)
    			{
    				ArrayList<Integer> arr=new ArrayList<Integer>();
    				arr=graph.get(parent);
    				visited[parent]=true;
    				for(int i=0;i<arr.size();i++)
    				{
    					int num=(int)arr.get(i);
    					if(visited[num]==false)
    					{
    						dfs(num,visited,dp);
    					}
    					dp[parent]=Math.max(dp[num]+1,dp[parent]);
    				}
    			}
    		//	static int flag1=0;
    			static int[] dis;
    			static int mod=1000000007;
    			static ArrayList<ArrayList<Integer>> graph;
    			
    			public static void bfs(int num,int size)
    			{
    				boolean[] visited=new boolean[size+1];
    				Queue<Integer> q=new LinkedList<>();
    				q.add(num);
    				ans[num]=1;
    				visited[num]=true;
    				while(!q.isEmpty())
    				{
    					int x=q.poll();
    					ArrayList<Integer> al=graph.get(x);
    					for(int i=0;i<al.size();i++)
    					{
    						int y=al.get(i);	
    						if(visited[y]==false)
    						{
    							q.add(y);
    							ans[y]=ans[x]+1;
    							visited[y]=true;
    						}
    					}
    				}
    			}
    			static int[] ans;
    			
    			
    			
    			
    			
    			
    			
    			
    			
    		//	static int[] a;			  
    			public static int[] sort(int[] a)
    			{
    				int n=a.length;
    				ArrayList<Integer> ar=new ArrayList<>();
    				for(int i=0;i<a.length;i++)
    				{
    					ar.add(a[i]);
    				}
    				Collections.sort(ar);
    				for(int i=0;i<n;i++)
    				{
    					a[i]=ar.get(i);
    				}
    				return a;
    			}
    			static public void main(String args[])throws IOException
    			{
    				int[] a=new int[4];
    				for(int i=0;i<4;i++)
    				{
    					a[i]=i();
    				}
    				int[] b=new int[4];
    				for(int i=0;i<4;i++)
    					b[i]=i();
    				int[] c=new int[4];
    				for(int i=0;i<4;i++)
    					c[i]=i();
    				long area1 = (long)Math.abs(a[0]-a[2])*(long)Math.abs(a[1]-a[3]); 
    				long ans=overlappingArea(a,b);
    				long ans1=overlappingArea(a,c);
    				long ans2=overlappingArea(b,c);
					if(ans==0)
    				{
    					if(ans1==0)
    					{
    						pln("YES");
    					}
    					else
    					{
    						long ans3=ans1;
    						if(ans1==area1)
    							pln("NO");
    						else
    							pln("YES");
    					}
    				}
    				else if(ans1==0)
    				{
    					if(ans==0)
    					{
    						pln("YES");
    					}
    					else
    					{
    						long ans3=ans;
    						if(ans==area1)
    							pln("NO");
    						else
    							pln("YES");
    					}
    				}
    				else if(ans!=0 && ans1!=0)
    				{
    					if(ans2<0)
    						ans2=0;
    					if(ans2==0)
    					{
    						long ans3=ans+ans1;
    						if(ans3==area1)
    							pln("NO");
    						else
    							pln("YES");
    					}
    					else
    					{
    						
    						b=FindPoints(a,b);
    						c=FindPoints(a,c);
    						ans2=overlappingArea(b,c);
    						if(b[0]==-1 || c[0]==-1)
    						{
    							ans2=0;
    						}
    						if(ans2<0)
    							ans2=0;
    						long ans3=ans+ans1-ans2;
    						if(ans3==area1)
    							pln("NO");
    						else
    							pln("YES");
    					}
    				}
    				
    			}
    			static int[] FindPoints(int[] a, int[] b) 
    			{ 
    				int[] ans=new int[4];
    				ans[0]=-1;
    				int x5 = Math.max(a[0], b[0]); 
    				int y5 = Math.max(a[1], b[1]); 
    			  
    				int x6 = Math.min(a[2], b[2]); 
    				int y6 = Math.min(a[3], b[3]); 
    			  
    				// no intersection 
    				if (x5 > x6 || y5 > y6)  
    				{ 
    					return ans; 
    				} 
    				ans[0]=x5;
    				ans[1]=y5;
    				ans[2]=x6;
    				ans[3]=y6;
    				return ans;
    			} 
    			static long overlappingArea(int[] a,int[] b) 
    			{ 
    				long area1 = (long)Math.abs(a[0]-a[2]) * 
    							(long)Math.abs(a[1]-a[3]); 
    			  
    				long area2 =(long)Math.abs(b[0]-b[2]) * 
    							(long)Math.abs(b[1]-b[3]); 
    			  
					long var1=(long)(Math.min(a[2],b[2])-Math.max(a[0],b[0]));
    				long var2=(long)(Math.min(a[3],b[3]) - 
    							 Math.max(a[1],b[1])); 
					if(var1<0 || var2<0)
						return 0;
					
					long areaI=var1*var2;
    				
					return ((areaI)); 
    			} 
    			
    			
    			/**/
    			static InputReader in=new InputReader(System.in);
    				static OutputWriter out=new OutputWriter(System.out);
    				public static long l()
    				{
    					String s=in.String();
    					return Long.parseLong(s);
    				}
    				public static void pln(String value)
    				{
    					System.out.println(value);
    				}
    				public static int i()
    				{
    					return in.Int();
    				}
    				public static String s()
    				{
    					return in.String();
    				}
    	}
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		 
    		class InputReader {
    			 
    			private InputStream stream;
    			private byte[] buf = new byte[1024];
    			private int curChar;
    			private int numChars;
    			private SpaceCharFilter filter;
    		 
    			public InputReader(InputStream stream) {
    				this.stream = stream;
    			}
    		 
    			public int read() {
    				if (numChars== -1)
    					throw new InputMismatchException();
    				if (curChar >= numChars) {
    					curChar = 0;
    					try {
    						numChars = stream.read(buf);
    					} catch (IOException e) {
    						throw new InputMismatchException();
    					}
    					if (numChars <= 0)
    						return -1;
    				}
    				return buf[curChar++];
    			}
    		 
    			public int Int() {
    				int c = read();
    				while (isSpaceChar(c))
    					c = read();
    				int sgn = 1;
    				if (c == '-') {
    					sgn = -1;
    					c = read();
    				}
    				int res = 0;
    				do {
    					if (c < '0' || c > '9')
    						throw new InputMismatchException();
    					res *= 10;
    					res += c - '0';
    					c = read();
    				} while (!isSpaceChar(c));
    				return res * sgn;
    			}
    		 
    			public String String() {
    				int c = read();
    				while (isSpaceChar(c))
    					c = read();
    				StringBuilder res = new StringBuilder();
    				do {
    					res.appendCodePoint(c);
    					c = read();
    				} while (!isSpaceChar(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;
    			}
    		 
    			public String next() {
    				return String();
    			}
    		 
    			public interface SpaceCharFilter {
    				public boolean isSpaceChar(int ch);
    			}
    		}
    		 
    		class OutputWriter {
    			private final PrintWriter writer;
    		 
    			public OutputWriter(OutputStream outputStream) {
    				writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    			}
    		 
    			public OutputWriter(Writer writer) {
    				this.writer = new PrintWriter(writer);
    			}
    		 
    			public void print(Object...objects) {
    				for (int i = 0; i < objects.length; i++) {
    					if (i != 0)
    						writer.print(' ');
    					writer.print(objects[i]);
    				}
    			}
    		 
    			public void printLine(Object...objects) {
    				print(objects);
    				writer.println();
    			}
    		 
    			public void close() {
    				writer.close();
    			}
    		 
    			public void flush() {
    				writer.flush();
    			}
    		 
    			}
    		 
    			class IOUtils {
    		 
    			public static int[] readIntArray(InputReader in, int size) {
    				int[] array = new int[size];
    				for (int i = 0; i < size; i++)
    					array[i] = in.Int();
    				return array;
    			}
    		 
    			} 