Quick sort is based on the Divide-and-conquer approach. In QuickSort(A, p, r), first, a procedure Partition(A, p, r) divides an array A[p..r] into two subarrays A[p..q-1] and A[q+1..r] such that each element of A[p..q-1] is less than or equal to A[q], which is, inturn, less than or equal to each element of A[q+1..r]. It also computes the index q.

In the conquer processes, the two subarrays A[p..q-1] and A[q+1..r] are sorted by recursive calls of QuickSort(A, p, q-1) and QuickSort(A, q+1, r).

Your task is to read a sequence A and perform the Partition based on the following pseudocode:


Partition(A, p, r)
1 x = A[r]
2 i = p-1
3 for j = p to r-1
4     do if A[j] <= x
5        then i = i+1
6            exchange A[i] and A[j]
7 exchange A[i+1] and A[r]
8 return i+1


Note that, in this algorithm, Partition always selects an element A[r] as a pivot element around which to partition the array A[p..r].

Constraints

* 1 ≤ n ≤ 100,000
* 0 ≤ Ai ≤ 100,000

Input

The first line of the input includes an integer n, the number of elements in the sequence A.

In the second line, Ai (i = 1,2,...,n), elements of the sequence are given separated by space characters.

Output

Print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character. The element which is selected as the pivot of the partition should be indicated by [  ].

Example

Input

12
13 19 9 5 12 8 7 4 21 2 6 11


Output

9 5 8 7 4 2 6 [11] 21 13 19 12
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class Main {
	public static void main(String[] args) throws NumberFormatException, IOException {
		ContestScanner scan = new ContestScanner();

		final int n = scan.nextInt();
		final int[] Ai = scan.nextIntArray(n);

		(new Solve(n, Ai)).solve();
	}
}
class Solve {
	private int n;
	private int[] Ai;

	public Solve(final int n, final int[] Ai)
	{
		this.n = n;
		this.Ai = Ai;
	}

	public void solve()
	{
		int[] A = Ai.clone();

		int q = partition(A, 0, n - 1);

		StringBuilder sb = new StringBuilder();

		for(int i=0; i < n; i++)
		{
			if(i == q) sb.append("[" + A[i] + "]");
			else sb.append(A[i]);
			if(i < n - 1) sb.append(" ");
		}

		System.out.println(sb.toString());
	}

	public int partition(int[] A, int p, final int r)
	{
		int x = A[r];
		int i = p - 1;
		for(int j=p; j < r; j++)
		{
			if(A[j] <= x)
			{
				++i;
				int tmp = A[j];
				A[j] = A[i];
				A[i] = tmp;
			}
		}
		int tmp = A[r];
		A[r] = A[i + 1];
		A[i + 1] = tmp;

		return i + 1;
	}
}
class ContestScanner {
	BufferedReader reader;
	String[] line;
	int index;
	public ContestScanner() {
		reader = new BufferedReader(new InputStreamReader(System.in));
	}

	public ContestScanner(String filename) throws FileNotFoundException {
		reader = new BufferedReader(new InputStreamReader(new FileInputStream(filename)));
	}

	public static interface ICreator<T> {
		public T createFromToken(final ContestScanner scanner) throws IOException;
	}

	public static interface IArrayInitializer {
		public void initialize(final ContestScanner scanner, final int i) throws IOException;
	}

	public static interface IObjectInitializer<T> {
		public T initialValue(final ContestScanner scanner);
	}

	public static class ObjectArrayInitializer<T> implements IArrayInitializer {
		protected T[] arr;
		protected final IObjectInitializer<T> initializer;

		private ObjectArrayInitializer(T[] arr, final IObjectInitializer<T> initializer)
		{
			this.arr = arr;
			this.initializer = initializer;
		}

		public static <T> ObjectArrayInitializer<T> create(T[] arr, final IObjectInitializer<T> initializer)
		{
			return new ObjectArrayInitializer<T>(arr, initializer);
		}

		public void initialize(final ContestScanner scanner, final int i) throws IOException {
			this.arr[i] = initializer.initialValue(scanner);
		}

		public T[] getArray()
		{
			return this.arr;
		}
	}


	public static class ByteArrayInitializer implements IArrayInitializer {
		protected byte[] arr;

		private ByteArrayInitializer(final int n)
		{
			this.arr = new byte[n];
		}

		public void initialize(final ContestScanner scanner, final int i) throws IOException {
			this.arr[i] = scanner.nextByte();
		}

		public byte[] getArray()
		{
			return this.arr;
		}
	}

	public static class ShortArrayInitializer implements IArrayInitializer {
		protected short[] arr;

		private ShortArrayInitializer(final int n)
		{
			this.arr = new short[n];
		}

		public void initialize(final ContestScanner scanner, final int i) throws IOException {
			this.arr[i] = scanner.nextShort();
		}

		public short[] getArray()
		{
			return this.arr;
		}
	}

	public static class IntArrayInitializer implements IArrayInitializer {
		protected int[] arr;

		private IntArrayInitializer(final int n)
		{
			this.arr = new int[n];
		}

		public void initialize(final ContestScanner scanner, final int i) throws IOException {
			this.arr[i] = scanner.nextInt();
		}

		public int[] getArray()
		{
			return this.arr;
		}
	}

	public static class LongArrayInitializer implements IArrayInitializer {
		protected long[] arr;

		private LongArrayInitializer(final int n)
		{
			this.arr = new long[n];
		}

		public void initialize(final ContestScanner scanner, final int i) throws IOException {
			this.arr[i] = scanner.nextLong();
		}

		public long[] getArray()
		{
			return this.arr;
		}
	}

	public static class FloatArrayInitializer implements IArrayInitializer {
		protected float[] arr;

		private FloatArrayInitializer(final int n)
		{
			this.arr = new float[n];
		}

		public void initialize(final ContestScanner scanner, final int i) throws IOException {
			this.arr[i] = scanner.nextFloat();
		}

		public float[] getArray()
		{
			return this.arr;
		}
	}

	public static class DoubleArrayInitializer implements IArrayInitializer {
		protected double[] arr;

		private DoubleArrayInitializer(final int n)
		{
			this.arr = new double[n];
		}

		public void initialize(final ContestScanner scanner, final int i) throws IOException {
			this.arr[i] = scanner.nextDouble();
		}

		public double[] getArray()
		{
			return this.arr;
		}
	}

	public String nextToken() throws IOException {
		if(line == null || index >= line.length)
		{
			line = reader.readLine().trim().split(" ");
			index = 0;
		}

		return line[index++];
	}

	public String next() throws IOException {
		return nextToken();
	}

	public String readLine() throws IOException {
		line = null;
		index = 0;

		return reader.readLine();
	}

	public byte nextByte() throws IOException, NumberFormatException {
		return Byte.parseByte(nextToken());
	}

	public short nextShort() throws IOException, NumberFormatException {
		return Short.parseShort(nextToken());
	}

	public int nextInt() throws IOException, NumberFormatException {
		return Integer.parseInt(nextToken());
	}

	public long nextLong() throws IOException, NumberFormatException {
		return Long.parseLong(nextToken());
	}

	public float nextFloat() throws IOException, NumberFormatException {
		return Float.parseFloat(nextToken());
	}

	public double nextDouble() throws IOException, NumberFormatException {
		return Double.parseDouble(nextToken());
	}

	public <T> T nextObject(final ICreator<T> creator) throws IOException, NumberFormatException {
		return creator.createFromToken(this);
	}

	public int[] nextIntArray(final int N) throws IOException, NumberFormatException {
		int[] result = new int[N];

		for(int i=0; i < N; i++) result[i] = nextInt();

		return result;
	}

	public long[] nextLongArray(final int N) throws IOException, NumberFormatException {
		long[] result = new long[N];

		for(int i=0; i < N; i++) result[i] = nextLong();

		return result;
	}

	public float[] nexFloatArray(final int N) throws IOException, NumberFormatException {
		float[] result = new float[N];

		for(int i=0; i < N; i++) result[i] = nextFloat();

		return result;
	}

	public double[] nexDoubleArray(final int N) throws IOException, NumberFormatException {
		double[] result = new double[N];

		for(int i=0; i < N; i++) result[i] = nextDouble();

		return result;
	}

	public <T> T[] nextObjectArray(T[] result, final ICreator<T> creator) throws IOException, NumberFormatException {
		for(int i=0, N=result.length; i < N; i++) result[i] = nextObject(creator);

		return result;
	}

	public <T> ArrayList<T> nextGenericObjectArrayList(final int N, final ICreator<T> creator) throws IOException, NumberFormatException {
		ArrayList<T> result = new ArrayList<T>();
		for(int i=0; i < N; i++) result.add(nextObject(creator));

		return result;
	}

	public void nextTable(final int N, IArrayInitializer... arrayInitializers) throws IOException, NumberFormatException {
		for(int i=0; i < N; i++) for(IArrayInitializer initializer: arrayInitializers)
		{
			initializer.initialize(this, i);
		}
	}
}