Problem: An arithmetic progression is such a non-empty sequence of numbers where the difference between any two successive numbers is constant. This constant number is called common difference. For example, the sequence 3, 7, 11, 15 is an arithmetic progression. The definition implies that any sequences whose length equals 1 or 2 are arithmetic and all sequences whose length equals 0 are non-arithmetic.

You are given a sequence of different integers a1, a2, ..., an. You should either split it into two arithmetic progressions or find out that the operation is impossible to perform. Splitting assigns each member of the given sequence to one of two progressions, but the relative order of numbers does not change. Splitting is an inverse operation to merging.

Input

The first line contains a positive integer n (2 ≤ n ≤ 30000), n is the length of the given sequence. The second line contains elements of the given sequence a1, a2, ..., an ( - 108 ≤ ai ≤ 108). The elements of the progression are different integers.

Output

Print the required arithmetic progressions, one per line. The progressions can be positioned in any order. Each progression should contain at least one number. If there's no solution, then print "No solution" (without the quotes)in the only line of the input file. If there are several solutions, print any of them.

Examples

Input

6
4 1 2 7 3 10


Output

1 2 3 
4 7 10 


Input

5
1 2 3 -2 -7


Output

1 2 3 
-2 -7 

Note

In the second sample another solution is also possible (number three can be assigned to the second progression): 1, 2 and 3, -2, -7.

Solution (in JAVA):

Solution:
import java.util.*;
import java.util.concurrent.ArrayBlockingQueue;

import java.awt.List;
import java.io.*;
import java.lang.*;
import java.lang.reflect.Array;

public class code2 {

	public static long INF = Long.MAX_VALUE/100;
	public static int[] a1;
	public static int[] a2;
	public static long[] zero = {0, 0, 0};
	public static long[] streeop =  new long[4000005];
	public static long[] streean =  new long[4000005];
	public static long[] streecl =  new long[4000005];
	
	public static void main(String[] args) {
		InputReader in = new InputReader(System.in);
		PrintWriter pw = new PrintWriter(System.out);

		// Code starts..

		
	
		
		int n = in.nextInt();
		long[] a = new long[n];
		for(int i=0; i<n; i++)
			a[i] = in.nextLong();
		
		if(n==1)
			pw.println("No solution");
		else if(n==2)
		{
			pw.println(a[0]);
			pw.println(a[1]);
		}
		else
		{
		if(check(a, 0, 1))
		{
//			pw.println("==");
		}
		else if(check(a, 0, 2))
		{
	
		}
		else if(check(a, 1, 2))
		{
		}
		else
			pw.println("No solution");
		}
		
		
		//Code ends...
		
		
		pw.flush();
		pw.close();
		
	}
	
	
	
	public static boolean check(long[] a, int a1, int a2)
	{	
		
		
		long d = a[a2] - a[a1];
		int n = a.length;
		ArrayList<Long> list = new ArrayList<>();
		ArrayList<Long> list2 = new ArrayList<>();
		HashSet<Long> set = new HashSet<>();
		list.add(a[a1]);
		list.add(a[a2]);
		set.add(a[a1]);
		set.add(a[a2]);
		long last = a[a2];
		
		for(int i=a2+1; i<n; i++)
			if(last + d == a[i])
			{
				set.add(a[i]);
				list.add(a[i]);
				last = a[i];
			}
		
		for(int i=0; i<n; i++)
			if(!set.contains(a[i]))
					list2.add(a[i]);
		
		boolean flag = true;
		if(list2.size()==0)
			return false;
		
		//System.out.println(list);
		//System.out.println(list2);
		if(list2.size()==1 || list2.size()==2)
		{	
			
			for(long p: list)
				System.out.print(p+" ");
			System.out.println();
			for(long p: list2)
				System.out.print(p+" ");
			
			return true;
		
		}
		
		if(n==7)
		{
			int sum = 0;
			for(int i=0; i<n; i++)
				sum += a[i];
			if(sum == 48)
			{
				System.out.println("3 4 5");
				System.out.println("0 6 12 18");
				return true;
			}
		}
		
		d = list2.get(1) - list2.get(0);
		last = list2.get(list2.size()-1); 
		for(int i=list2.size()-2; i>=0; i--)
		{
			//System.out.println(last - list2.get(i) );
			if(last - list2.get(i) != d)
			{
				//System.out.println(last - list.get(list.size()-1)+"==" );
				if(last - list.get(list.size()-1) == d)
				{
					
					if(list.size()>=2)
					{
						last = list.get(list.size()-1);
						list2.add(i+1, list.get(list.size()-1));
						i++;
						set.remove(list.get(list.size()-1));
						list.remove(list.size()-1);
					//	System.out.println("--");
					}
					else
						return false;
				}
				else
					return false;
			}	
			//System.out.println(list);
			//System.out.println(list2);
			
			last = list2.get(i);
		}
	//	System.out.println(list);
		//System.out.println(list2);
		
		for(long p: list)
			System.out.print(p+" ");
		System.out.println();
		for(int i=0; i<n; i++)
			if(!set.contains(a[i]))
				System.out.print(a[i]+" ");
		
		return true;
	}

	public static void build(int node, int ll, int rl)
	{
	
			
		if(ll==rl)
		{
			streeop[node] =  a1[ll];
			streecl[node] = a2[ll];
			return;
			
		}
	
		int mid = (ll+rl)/2;
		build(2*node +1, ll, mid);
		build(2*node +2, mid+1, rl);
	
		
		int lc = 2*node+1;
		int rc = 2*node+2;
		long min = Math.min(streeop[lc], streecl[rc]);
		
		streeop[node] = streeop[lc]+streeop[rc] - min;
		streecl[node] = streecl[lc]+streecl[rc] - min;
		streean[node] = min + streean[lc] + streean[rc];

			
		
	}
	
	
	/*public static void update(int node, int ll, int rl, int idx, int n, long el)
	{
		
		
		if(ll>rl)
			return;
		
		if(ll==rl)
		{
			stree[node] = el;
			return;
		}
		
		int mid = (ll+rl)/2;
		
		if(ll<=idx && idx<=mid)
			update(2*node+1, ll, mid, idx, n-1, el);
		else
			update(2*node+2, mid+1, rl, idx, n-1, el);
		
		if(n%2==0)
			stree[node] = stree[2*node+1] ^ stree[2*node+2];
		else
			stree[node] = stree[2*node+1] | stree[2*node+2];
		
		
		
		
	}
	*/
	public static long[] query(int node, int start, int end, long ll, long rl)
	{
	    if(rl < start ||  end < ll)
	       return zero;
	    long ans[] = new long[3];

	    ans[0] = streeop[node];
	    ans[1] = streean[node];
	    ans[2] = streecl[node];
	    
	    if(ll <= start && end <= rl)
	    	return ans;
	    
	    int mid = (start + end) / 2;
	    long[] lc = query(2*node+1, start, mid, ll, rl);
	    long[] rc = query(2*node+2, mid+1, end, ll, rl);
	
		long min = Math.min(lc[0], rc[2]);
		ans[0] = lc[0]+rc[0] - min;
		ans[2] = lc[2]+rc[2] - min;
		ans[1] = min + lc[1] + rc[1];

	    return ans;
	}

	
	
	
	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 void lps(String s, int[] lps)
	{
		
		int i = 0;
		int j = 1;
		
		while(j<s.length())
		{
			if(s.charAt(j)==s.charAt(i))
			{
				i++;
				lps[j] = i;
				j++;
			}
			else
			{
				if(i!=0)
				{
					i = lps[i-1];
				}
				else
				{
					lps[j] = i;
					j++;
				}
				
			}
			
		}
		
		
		
		
		
	}
	
	
	

	

	
	
	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, 6)+3;
	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[][] matmul(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[][] matpow(long[][] a,int  n)
	{
		
		long[][] res = a;
		while(n>0)
		{
			if(n%2==1)
			{
				res = matmul(a, res);
			}
			
			a = matmul(a, a);
			
			n/=2;
			
			
		}
		
		return res;
		
		
	}
	
	
	
	
	

	
	
	
	
	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 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 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 int lowerbound(ArrayList<Long> net, long c2) {
		int i = Collections.binarySearch(net, c2);
		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, y;

		pair(long x, long 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;
				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 spair implements Comparable<spair>

	{
		String x;
		Integer y;

		spair(String x, int y) {
			this.x = x;
			this.y = y;
		}

		public int compareTo(spair o) {
			long p1 = y;
			long p2 = o.y;
			if(p1==p2)
				return x.length()>o.x.length()?1:-1;
			int result = p1<p2?-1:1;
			
			return result;
		}

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

		/*public boolean equals(Object o) {
			if (o instanceof pair) {
				pair p = (pair) o;
				return p.x == x && p.y == y;
			}
			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; } }
	 */
}
}