Snuke has an empty sequence a.

He will perform N operations on this sequence.

In the i-th operation, he chooses an integer j satisfying 1 \leq j \leq i, and insert j at position j in a (the beginning is position 1).

You are given a sequence b of length N. Determine if it is possible that a is equal to b after N operations. If it is, show one possible sequence of operations that achieves it.

Constraints

* All values in input are integers.
* 1 \leq N \leq 100
* 1 \leq b_i \leq N

Input

Input is given from Standard Input in the following format:


N
b_1 \dots b_N


Output

If there is no sequence of N operations after which a would be equal to b, print `-1`. If there is, print N lines. In the i-th line, the integer chosen in the i-th operation should be printed. If there are multiple solutions, any of them is accepted.

Examples

Input

3
1 2 1


Output

1
1
2


Input

2
2 2


Output

-1


Input

9
1 1 1 2 2 1 2 3 2


Output

1
2
2
3
1
2
2
1
1
import java.io.*;
import java.math.*;
import java.util.*;
import java.util.stream.*;

public class Main {

	void submit() {
		int n = nextInt();
		int[] inv = new int[n];
		for (int i = 0; i < n; i++) {
			inv[i] = nextInt() - 1;
		}
		
		for (int i = 0; i < n; i++) {
			if (inv[i] > i) {
				out.println(-1);
				return;
			}
		}
		
		ArrayList<Integer> all = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			all.add(i);
		}
		
		int[] perm = new int[n];
		for (int i = n - 1; i >= 0; i--) {
			int idx = all.size() - 1 - inv[i];
			
			perm[i] = all.get(idx);
			all.remove(idx);
		}
		
		int[] ans = new int[n];
		for (int i = 0; i < n; i++) {
			ans[perm[i]] = inv[i];
		}
		
		for (int i = n - 1; i >= 0; i--) {
			out.println((ans[i] + 1));
		}
		
	}

	void test() {

	}

	void stress() {
		for (int tst = 0;; tst++) {
			if (false) {
				throw new AssertionError();
			}
			System.err.println(tst);
		}
	}

	Main() throws IOException {
		is = System.in;
		out = new PrintWriter(System.out);
		submit();
		// stress();
		// test();
		out.close();
	}

	static final Random rng = new Random();
	static final int C = 5;

	static int rand(int l, int r) {
		return l + rng.nextInt(r - l + 1);
	}

	public static void main(String[] args) throws IOException {
		new Main();
	}

	private InputStream is;
	PrintWriter out;

	private byte[] buf = new byte[1 << 14];
	private int bufSz = 0, bufPtr = 0;

	private int readByte() {
		if (bufSz == -1)
			throw new RuntimeException("Reading past EOF");
		if (bufPtr >= bufSz) {
			bufPtr = 0;
			try {
				bufSz = is.read(buf);
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
			if (bufSz <= 0)
				return -1;
		}
		return buf[bufPtr++];
	}

	private boolean isTrash(int c) {
		return c < 33 || c > 126;
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isTrash(b))
			;
		return b;
	}

	String nextToken() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!isTrash(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	String nextString() {
		int b = readByte();
		StringBuilder sb = new StringBuilder();
		while (!isTrash(b) || b == ' ') {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	double nextDouble() {
		return Double.parseDouble(nextToken());
	}

	char nextChar() {
		return (char) skip();
	}

	int nextInt() {
		int ret = 0;
		int b = skip();
		if (b != '-' && (b < '0' || b > '9')) {
			throw new InputMismatchException();
		}
		boolean neg = false;
		if (b == '-') {
			neg = true;
			b = readByte();
		}
		while (true) {
			if (b >= '0' && b <= '9') {
				ret = ret * 10 + (b - '0');
			} else {
				if (b != -1 && !isTrash(b)) {
					throw new InputMismatchException();
				}
				return neg ? -ret : ret;
			}
			b = readByte();
		}
	}

	long nextLong() {
		long ret = 0;
		int b = skip();
		if (b != '-' && (b < '0' || b > '9')) {
			throw new InputMismatchException();
		}
		boolean neg = false;
		if (b == '-') {
			neg = true;
			b = readByte();
		}
		while (true) {
			if (b >= '0' && b <= '9') {
				ret = ret * 10 + (b - '0');
			} else {
				if (b != -1 && !isTrash(b)) {
					throw new InputMismatchException();
				}
				return neg ? -ret : ret;
			}
			b = readByte();
		}
	}
}
