Problem: Ivan is a novice painter. He has n dyes of different colors. He also knows exactly m pairs of colors which harmonize with each other.

Ivan also enjoy playing chess. He has 5000 rooks. He wants to take k rooks, paint each of them in one of n colors and then place this k rooks on a chessboard of size 10^{9} × 10^{9}.

Let's call the set of rooks on the board connected if from any rook we can get to any other rook in this set moving only through cells with rooks from this set. Assume that rooks can jump over other rooks, in other words a rook can go to any cell which shares vertical and to any cell which shares horizontal.

Ivan wants his arrangement of rooks to have following properties:

  * For any color there is a rook of this color on a board;
  * For any color the set of rooks of this color is connected;
  * For any two different colors a b union of set of rooks of color a and set of rooks of color b is connected if and only if this two colors harmonize with each other.



Please help Ivan find such an arrangement.

Input

The first line of input contains 2 integers n, m (1 ≤ n ≤ 100, 0 ≤ m ≤ min(1000,    (n(n-1))/(2))) — number of colors and number of pairs of colors which harmonize with each other.

In next m lines pairs of colors which harmonize with each other are listed. Colors are numbered from 1 to n. It is guaranteed that no pair occurs twice in this list.

Output

Print n blocks, i-th of them describes rooks of i-th color.

In the first line of block print one number a_{i} (1 ≤ a_{i} ≤ 5000) — number of rooks of color i. In each of next a_{i} lines print two integers x and y (1 ≤ x,    y ≤ 10^{9}) — coordinates of the next rook.

All rooks must be on different cells.

Total number of rooks must not exceed 5000.

It is guaranteed that the solution exists.

Examples

Input

3 2
1 2
2 3


Output

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


Input

3 3
1 2
2 3
3 1


Output

1
1 1
1
1 2
1
1 3


Input

3 1
1 3


Output

1
1 1
1
2 2
1
3 1

Note

Rooks arrangements for all three examples (red is color 1, green is color 2 and blue is color 3).

<image>

<image>

<image>

Solution (in JAVA):

Solution:
import java.util.*;
import java.awt.List;
import java.io.*;
import java.lang.*;
import java.lang.reflect.Array;

public class Code3 {
	
		
		
		public static void main(String[] args) throws FileNotFoundException {
		
		
		InputReader in = new InputReader(System.in);
		PrintWriter pw = new PrintWriter(System.out);

		// Code starts..
		
		
		
		int[][] a = new int[101][101];
		int n = in.nextInt();
		int m = in.nextInt();
		ArrayList<Integer>[] adj = new ArrayList[101];
		for(int i=0; i<101; i++)
			adj[i] = new ArrayList<>();
		
		for(int i=0; i<m; i++)
		{
			
			int u = in.nextInt();
			int v = in.nextInt();
			adj[Math.min(u, v)].add(Math.max(u, v));
			
		}
		
		
		/*for(int i=1; i<=n; i++)
		{
			a[i][i] = i;
			for(int p: adj[i])
				a[i][p] = i;
		}
		*/
		
		ArrayList<Integer>[] list = new ArrayList[101];
		for(int i=0; i<101; i++)
			list[i] = new ArrayList<>();
		
		
		for(int i=1; i<=n; i++)
		{
		
			//for(int k=0; k<i; k++)
			//	list.add(k*n  + i);
			
			for(int p: adj[i])
			{
				list[i].add((i-1)*n + p);
				list[p].add((i-1)*n + p);
			}
			/*pw.println(2*list.size() + 1);
			pw.println(i+" "+((i-1)*n + i));
			for(int p: list)
			{
				pw.println(i+" "+p);
				pw.println(p%n==0?n : p%n+" "+p);
			}
			*/
		}
		
		for(int i=1; i<=n; i++)
		{
			if(list[i].size()>0)
			{
			pw.println(list[i].size());
			for(int p: list[i])
				pw.println(i+" "+p);
			}
			else
			{
				pw.println(1);
				pw.println(i+" "+((i-1)*n + i));
			}
		}
		
		
        // code ends...

		pw.flush();
		pw.close();
	}


	

	  
	
	public 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 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 c = 0;

	public static long mod = (long)Math.pow(10, 9)+7;
	public static int d;
	public static int p;
	public static int q;
	public static boolean flag;
	//public static long INF = Long.MAX_VALUE;

	public static void factSieve(int[] fact, long n) {

		for (int i = 2; i <= n; i += 2)
			fact[i] = 2;

		for (int i = 3; i <= n; i += 2) {
			if (fact[i] == 0) {
				fact[i] = i;

				for (int j = i; (long) j * i <= n; j++) {
					fact[(int) ((long) i * j)] = i;
				}
			}
		}

		/*
		 * int k = 1000; while(k!=1) { System.out.print(a[k]+" "); k /= a[k];
		 * 
		 * }
		 */
	}

	public static long floorsqrt(long n) {
		long ans = 0;
		long l = 0;
		long r = n;
		long mid = 0;
		while (l <= r) {
			mid = (l + r) / 2;
			if (mid * mid == n)
				return mid;

			if (mid * mid > n) {
				r = mid - 1;
			} else {
				ans = mid;
				l = mid + 1;
			}

		}

		return ans;
	}

	public static long fun(int[] a, int[] b, int m, int n) {
		long result = 0;
		for (int i = 0; i < m; i++)
			for (int j = 0; j < m; j++) {
				long[] fib = new long[Math.max(2, n + 2)];
				fib[1] = a[i];
				fib[2] = b[j];
				for (int k = 3; k <= n; k++)
					fib[k] = (fib[k - 1] % mod + fib[k - 2] % mod) % mod;
				result = (result % mod + fib[n] % mod) % mod;
			}

		return result;

	}

	/*
	 * public static double slope(pair p1, pair p2) { double m = INF; if((p1.x -
	 * p2.x)!=0) m = p1.y - p2.y/(p1.x - p2.x);
	 * 
	 * 
	 * return Math.abs(m);
	 * 
	 * }
	 */

	public static int gcd(int p2, int p22) {
		if (p2 == 0)
			return (int) p22;
		return gcd(p22 % p2, p2);
	}

	public static int findGCD(int arr[], int n) {
		int result = arr[0];
		for (int i = 1; i < n; i++)
			result = gcd(arr[i], result);

		return result;
	}

	public static void nextGreater(long[] a, int[] ans) {

		Stack<Integer> stk = new Stack<>();
		stk.push(0);

		for (int i = 1; i < a.length; i++) {

			if (!stk.isEmpty()) {
				int s = stk.pop();
				while (a[s] < a[i]) {
					ans[s] = i;
					if (!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if (a[s] >= a[i])
					stk.push(s);
			}

			stk.push(i);

		}
		return;

	}

	public static void nextGreaterRev(long[] a, int[] ans) {

		int n = a.length;
		int[] pans = new int[n];
		Arrays.fill(pans, -1);
		long[] arev = new long[n];
		for (int i = 0; i < n; i++)
			arev[i] = a[n - 1 - i];

		Stack<Integer> stk = new Stack<>();
		stk.push(0);

		for (int i = 1; i < n; i++) {

			if (!stk.isEmpty()) {
				int s = stk.pop();
				while (arev[s] < arev[i]) {
					pans[s] = n - i - 1;
					if (!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if (arev[s] >= arev[i])
					stk.push(s);
			}

			stk.push(i);

		}

		// for(int i=0; i<n; i++)
		// System.out.print(pans[i]+" ");

		for (int i = 0; i < n; i++)
			ans[i] = pans[n - i - 1];

		return;

	}


	public static void nextSmallerRev(int[] a, int[] ans) {

		int n = a.length;
		int[] pans = new int[n];
		Arrays.fill(pans, -1);
		long[] arev = new long[n];
		for (int i = 0; i < n; i++)
			arev[i] = a[n - 1 - i];

		Stack<Integer> stk = new Stack<>();
		stk.push(0);

		for (int i = 1; i < n; i++) {

			if (!stk.isEmpty()) {
				int s = stk.pop();
				while (arev[s] > arev[i]) {
					pans[s] = n - i - 1;
					if (!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if (arev[s] <= arev[i])
					stk.push(s);
			}

			stk.push(i);

		}

		// for(int i=0; i<n; i++)
		// System.out.print(pans[i]+" ");

		for (int i = 0; i < n; i++)
			ans[i] = pans[n - i - 1];

		return;

	}

	
	public static void nextSmaller(int[] a, int[] ans) {

		Stack<Integer> stk = new Stack<>();
		stk.push(0);

		for (int i = 1; i < a.length; i++) {

			if (!stk.isEmpty()) {
				int s = stk.pop();
				while (a[s] > a[i]) {
					ans[s] = i;
					if (!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if (a[s] <= a[i])
					stk.push(s);
			}

			stk.push(i);

		}
		return;

	}


	public static long[][] mul(long[][] a, long[][] b){
		
		
		int n = a.length;
		int m = b[0].length;
		long[][] c = new long[n][m];
		
		for(int i=0; i<n; i++)
			for(int j=0; j<m; j++)
			{
				long tmp = 0;
				for(int k=0; k<a[0].length; k++)
					tmp =( (tmp+mod)%mod+(a[i][k]*b[k][j]+mod)%mod)%mod;
				c[i][j] = (tmp+mod)%mod;
			}
		
		return c;
	}
	
	
	
	
	public static long lcm(int[] numbers) {
		long lcm = 1;
		int divisor = 2;
		while (true) {
			int cnt = 0;
			boolean divisible = false;
			for (int i = 0; i < numbers.length; i++) {
				if (numbers[i] == 0) {
					return 0;
				} else if (numbers[i] < 0) {
					numbers[i] = numbers[i] * (-1);
				}
				if (numbers[i] == 1) {
					cnt++;
				}
				if (numbers[i] % divisor == 0) {
					divisible = true;
					numbers[i] = numbers[i] / divisor;
				}
			}
			if (divisible) {
				lcm = lcm * divisor;
			} else {
				divisor++;
			}
			if (cnt == numbers.length) {
				return lcm;
			}
		}
	}

	public static long fact(long n) {

		long factorial = 1;
		for (int i = 1; i <= n; i++) {
			factorial *= i;
		}
		return factorial;
	}
	
	
	


	public static int lowerLimit(int[] a, int n) {
		int ans = 0;

		int ll = 0;
		int rl = a.length - 1;
		// System.out.println(a[rl]+" "+n);
		if (a[0] > n)
			return 0;
		if (a[0] == n)
			return 1;
		else if (a[rl] <= n)
			return rl + 1;

		while (ll <= rl) {

			int mid = (ll + rl) / 2;
			if (a[mid] == n) {
				ans = mid + 1;
				break;
			}

			else if (a[mid] > n) {
				rl = mid - 1;

			} else {
				ans = mid + 1;
				ll = mid + 1;
			}
		}

		return ans;
	}
	public static long choose(long total, long choose) {
		if (total < choose)
			return 0;
		if (choose == 0 || choose == total)
			return 1;
		return (choose(total - 1, choose - 1) + choose(total - 1, choose)) % mod;
	}

	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 int floorSearch(int arr[], int low, int high, int x) {
		if (low > high)
			return -1;

		if (x > arr[high])
			return high;
		int mid = (low + high) / 2;

		if (mid > 0 && arr[mid - 1] < x && x < arr[mid])
			return mid - 1;

		if (x < arr[mid])
			return floorSearch(arr, low, mid - 1, x);

		return floorSearch(arr, mid + 1, high, x);
	}

	public static void swap(int a, int b) {
		int temp = a;
		a = b;
		b = temp;
	}

	public static ArrayList<Integer> primeFactorization(int n) {
		ArrayList<Integer> a = new ArrayList<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 void print(int[] a)
	{
		PrintWriter pw = new PrintWriter(System.out);
		for(int i=0; i<a.length; i++)
			pw.print(a[i]+" ");
		
		pw.println();
		pw.flush();
		pw.close();
		
	}
	
	public static void print(long[] a)
	{
		PrintWriter pw = new PrintWriter(System.out);
		for(int i=0; i<a.length; i++)
			pw.print(a[i]+" ");
		
		pw.println();
		pw.flush();
		pw.close();
		
	}
	
	

	public static int lowerbound(ArrayList<Long> list, long l) {
		int i = Collections.binarySearch(list, l);
		if (i < 0)
			i = -(i + 2);
		return i;

	}
	
	public static int lowerboundArray(int[] dis, int c2) {
		int i = Arrays.binarySearch(dis, c2);
		if (i < 0)
			i = -(i + 2);
		return i;

	}

	public static int uperbound(ArrayList<Integer> list, int c2) {
		int i = Collections.binarySearch(list, c2);
		if (i < 0)
			i = -(i + 1);
		return i;

	}

	public static int uperboundArray(int[] dis, int c2) {
		int i = Arrays.binarySearch(dis, c2);
		if (i < 0)
			i = -(i + 1);
		return i;

	}

	public static long[] sort(long[] a) {
		Random gen = new Random();
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int ind = gen.nextInt(n - i) + i;
			long temp = a[ind];
			a[ind] = a[i];
			a[i] = temp;
		}

		Arrays.sort(a);
		return a;
	}

	public static int[] sort(int[] a) {
		Random gen = new Random();
		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;
		}

		Arrays.sort(a);
		return a;
	}

	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;
	}

	public static int[] countDer(int n) {
		int der[] = new int[n + 1];

		der[0] = 1;
		der[1] = 0;
		der[2] = 1;

		for (int i = 3; i <= n; ++i)
			der[i] = (i - 1) * (der[i - 1] + der[i - 2]);

		// Return result for n
		return der;
	}

	static long binomialCoeff(int n, int k) {
		long C[][] = new long[n + 1][k + 1];
		int i, j;

		// Calculate value of Binomial Coefficient in bottom up manner
		for (i = 0; i <= n; i++) {
			for (j = 0; j <= Math.min(i, k); j++) {
				// Base Cases
				if (j == 0 || j == i)
					C[i][j] = 1;

				// Calculate value using previosly stored values
				else
					C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
			}
		}

		return C[n][k];
	}

	public static long binaryExponentiation(long x, long n) {
		long result = 1;
		while (n > 0) {
			if (n % 2 == 1)
				result = result * x;
			x = (x % mod * x % mod) % mod;
			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 sie(long A, long M) {
		return modularExponentiation(A, M - 2, M);
	}

	public static boolean checkYear(int year) {
		if (year % 400 == 0)
			return true;

		if (year % 100 == 0)
			return false;

		if (year % 4 == 0)
			return true;
		return false;
	}

	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 implements Comparable<pair>

	{
		Long x;
		Long y;

		pair(long ab, long m) {
			this.x = ab;
			this.y = m;
		}

		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;
				if(p.x-x==0 && p.y-y==0)
					return true;
				else
				return false;
			}
			return false;
		}

		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode();
		}

	}
	

	static class triplet implements Comparable<triplet> {
		Integer x, y, z;

		triplet(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}

		public int compareTo(triplet o) {
			int result = x.compareTo(o.x);
			if (result == 0)
				result = y.compareTo(o.y);
			if (result == 0)
				result = z.compareTo(o.z);

			return result;
		}

		public boolean equlas(Object o) {
			if (o instanceof triplet) {
				triplet p = (triplet) o;
				return x == p.x && y == p.y && z == p.z;
			}
			return false;
		}

		public String toString() {
			return x + " " + y + " " + z;
		}

		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode() + new Long(z).hashCode();
		}
	}

	
	static class query implements Comparable<query> {
		Integer l,r, x, idx, tp;

	
		query(int l, int r, int x, int id, int tp)
		{
			this.l = l ;
			this.r = r;
			this.x = x;
			this.idx = id;
			this.tp = tp;
		}
		
		public int compareTo(query o) {
			int result = x.compareTo(o.x);
			
			return result;
		}

		
	

		
	}
	
	/*
	 * static class node implements Comparable<node>
	 * 
	 * { Integer x, y, z; node(int x,int y, int z) { this.x=x; this.y=y; this.z=z; }
	 * 
	 * public int compareTo(pair o) { int result = x.compareTo(o.x); if(result==0)
	 * result = y.compareTo(o.y); if(result==0) result = z.compareTo(z); return
	 * result; }
	 * 
	 * @Override public int compareTo(node o) { // TODO Auto-generated method stub
	 * return 0; } }
	 */
}