Problem: A positive integer number n is written on a blackboard. It consists of not more than 105 digits. You have to transform it into a beautiful number by erasing some of the digits, and you want to erase as few digits as possible.

The number is called beautiful if it consists of at least one digit, doesn't have leading zeroes and is a multiple of 3. For example, 0, 99, 10110 are beautiful numbers, and 00, 03, 122 are not.

Write a program which for the given n will find a beautiful number such that n can be transformed into this number by erasing as few digits as possible. You can erase an arbitraty set of digits. For example, they don't have to go one after another in the number n.

If it's impossible to obtain a beautiful number, print -1. If there are multiple answers, print any of them.

Input

The first line of input contains n — a positive integer number without leading zeroes (1 ≤ n < 10100000).

Output

Print one number — any beautiful number obtained by erasing as few as possible digits. If there is no answer, print  - 1.

Examples

Input

1033


Output

33


Input

10


Output

0


Input

11


Output

-1

Note

In the first example it is enough to erase only the first digit to obtain a multiple of 3. But if we erase the first digit, then we obtain a number with a leading zero. So the minimum number of digits to be erased is two.

Solution (in JAVA):

Solution:
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.List;

public class Main {
	InputStream is;

	int __t__ = 1;
	int __f__ = 0;
	int __FILE_DEBUG_FLAG__ = __f__;
	String __DEBUG_FILE_NAME__ = "src/C2";

	FastScanner in;
	PrintWriter out;

	int INF = 1000000000;
	
	class State {
		int i, j, k;
		State(int i, int j, int k) {
			this.i = i;
			this.j = j;
			this.k = k;
		}
	}
	
	void dfs(String s, State[][][] prev, State u, StringBuilder result) {
		State v = prev[u.i][u.j][u.k];
		if (v.i != -1 && v.j != -1 && v.k != -1)
			dfs(s, prev, v, result);
		result.append(s.charAt(u.i));
	}
	
	String eraseLeadingZero(String s) {
		int firstNotZero = 0;
		while (firstNotZero < s.length() && s.charAt(firstNotZero) == '0') firstNotZero++;
		if (firstNotZero == s.length()) {
			return "0";
		}
		return s.substring(firstNotZero);
	}
	
	public void solve() {
		String _s = in.next();
		boolean existsZero = false;
		for (int i = 0; i < _s.length(); i++) {
			existsZero |= _s.charAt(i) == '0';
		}	

		String s = eraseLeadingZero(_s);
		
		int n = s.length();
		int[][][] dp = new int[n+1][3][2];
		State[][][] prev = new State[n+1][3][2];
		for (int i = 0; i <= n; i++) 
			for (int j = 0; j < 3; j++) 
				Arrays.fill(dp[i][j], INF);
		dp[0][0][0] = 0;
		prev[0][0][0] = new State(-1, -1, -1);
		
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < 3; j++) {
				for (int k = 0; k < 2; k++) {
					if (dp[i+1][j][k] > dp[i][j][k] + 1) {
						dp[i+1][j][k] = dp[i][j][k] + 1;
						prev[i+1][j][k] = prev[i][j][k];
					}
					
					int c = s.charAt(i) - '0';
					int nj = (j + c) % 3;
					int nk = Math.max(k, s.charAt(i) == '0' ? 0 : 1);
					int ncost = dp[i][j][k];
					if (k == 0 && nk == 0) ncost++;
					
					if (dp[i+1][nj][nk] > ncost) {
						dp[i+1][nj][nk] = ncost;
						prev[i+1][nj][nk] = new State(i, j, k);
					}				
				}
			}
		}
		
		if (dp[n][0][1] == INF) { 
			System.out.println(existsZero ? 0 : -1);
			return;
		}
		
		StringBuilder res = new StringBuilder();
		dfs(s, prev, prev[n][0][1], res);
		System.out.println(eraseLeadingZero(res.toString()));		
	}
	
	public void run() {
		if (__FILE_DEBUG_FLAG__ == __t__) {
			try {
				is = new FileInputStream(__DEBUG_FILE_NAME__);
			} catch (FileNotFoundException e) {
				// TODO ��ư�������줿 catch �֥�å�
				e.printStackTrace();
			}
			System.out.println("FILE_INPUT!");
		} else {
			is = System.in;
		}
		in = new FastScanner(is);
		out = new PrintWriter(System.out);

		solve();
	}

	public static void main(String[] args) {
		new Main().run();
	}

	public void mapDebug(int[][] a) {
		System.out.println("--------map display---------");

		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				System.out.printf("%3d ", a[i][j]);
			}
			System.out.println();
		}

		System.out.println("----------------------------");
		System.out.println();
	}

	public void debug(Object... obj) {
		System.out.println(Arrays.deepToString(obj));
	}

	class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FastScanner(InputStream stream) {
			this.stream = stream;
			//stream = new FileInputStream(new File("dec.in"));

		}

		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++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		int[] nextIntArray(int n) {
			return nextIntArray(n, 0);
		}

		int[] nextIntArray(int n, int margin) {
			int[] array = new int[n + margin];
			for (int i = 0; i < n; i++)
				array[i + margin] = nextInt();

			return array;
		}

		int[][] nextIntMap(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextIntArray(m);
			}
			return map;
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		long[] nextLongArray(int n) {
			return nextLongArray(n, 0);
		}

		long[] nextLongArray(int n, int margin) {
			long[] array = new long[n + margin];
			for (int i = 0; i < n; i++)
				array[i + margin] = nextLong();

			return array;
		}

		long[][] nextLongMap(int n, int m) {
			long[][] map = new long[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextLongArray(m);
			}
			return map;
		}

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

		double[] nextDoubleArray(int n) {
			return nextDoubleArray(n, 0);
		}

		double[] nextDoubleArray(int n, int margin) {
			double[] array = new double[n + margin];
			for (int i = 0; i < n; i++)
				array[i + margin] = nextDouble();

			return array;
		}

		double[][] nextDoubleMap(int n, int m) {
			double[][] map = new double[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextDoubleArray(m);
			}
			return map;
		}

		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();

			return array;
		}

		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}