Problem: One day Vasya was solving arithmetical problems. He wrote down an expression a + b = c in his notebook. When the teacher checked Vasya's work it turned out that Vasya had solved the problem incorrectly. Now Vasya tries to find excuses. He says that he simply forgot to write down several digits in numbers a, b and c, but he can't remember what numbers they actually were. Help Vasya, find such numbers x, y and z, with which the following conditions are met: 

  * x + y = z, 
  * from the expression x + y = z several digits can be erased in such a way that the result will be a + b = c, 
  * the expression x + y = z should have the minimal length. 

Input

The first and only input line contains the expression a + b = c (1 ≤ a, b, c ≤ 106, a, b and c don't contain leading zeroes) which is the expression Vasya wrote down.

Output

Print the correct expression x + y = z (x, y and z are non-negative numbers without leading zeroes). The expression a + b = c must be met in x + y = z as a subsequence. The printed solution should have the minimal possible number of characters. If there are several such solutions, you can print any of them.

Examples

Input

2+4=5


Output

21+4=25


Input

1+1=3


Output

1+31=32


Input

1+1=2


Output

1+1=2

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class A {


	public static void main(String[] args) throws IOException 
	{
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		String[] ops = sc.next().split("\\+|=");
		int sz = 8 * 8 * 8 * 10 * 8;
		int[] dist = new int[sz], p = new int[sz], pc1 = new int[sz], pc2 = new int[sz], pcs = new int[sz];
		Arrays.fill(dist, 100);
		PriorityQueue<Edge> q = new PriorityQueue<>();
		q.add(new Edge(0, 0));
		dist[0] = 0;
		int l1 = ops[0].length() - 1, l2 = ops[1].length() - 1, ls = ops[2].length() - 1;
		while(!q.isEmpty())
		{
			Edge e = q.remove();
			int cur = e.state % 5120, c = cur % 10, ds = cur / 10 % 8, d2 = cur / 80 % 8, d1 = cur / 640;
			int cc = e.state / 5120;
			if(e.cost > dist[e.state])
				continue;

			int p1 = d1 <= l1 ? ops[0].charAt(l1 - d1) - '0' : (cc & 1) == 0 ? -1 : 0;
			int p2 = d2 <= l2 ? ops[1].charAt(l2 - d2) - '0' : (cc & 2) == 0 ? -1 : 0;
			int ps = ds <= ls ? ops[2].charAt(ls - ds) - '0' : (cc & 4) == 0 ? -1 : 0;

			int nxt, c1, c2, cs, cost;
			for(int i = 0; i < 10; ++i)
				for(int j = 0; j < 10; ++j)
				{
					c1 = i == p1 ? 1 : 0;
					c2 = j == p2 ? 1 : 0;
					cs = (i + j + c) % 10 == ps ? 1 : 0;
					if((cc & 1-c1<<0) != 0 || (cc & 1-c2<<1) != 0 || (cc & 1-cs<<2) != 0)
						continue;
					int nxtCC = 0, nxtD1 = m(d1 + c1, l1 + 1), nxtD2 = m(d2 + c2, l2 + 1), nxtDS = m(ds + cs, ls + 1);
					if(nxtD1 == l1 + 1)
						nxtCC |= 1;
					if(nxtD2 == l2 + 1)
						nxtCC |= 2;
					if(nxtDS == ls + 1)
						nxtCC |= 4; 
					for(int k = 0; k < 8; ++k)
						if((k & cc) == cc && (k | nxtCC) == nxtCC)
						{
							nxt = get(nxtD1, nxtD2, nxtDS, (i + j + c) / 10, k);

							cost = e.cost + 3 - (c1 + c2 + cs);
							if(cost < dist[nxt])
							{
								q.add(new Edge(nxt, dist[nxt] = cost));
								p[nxt] = e.state;
								pc1[nxt] = c1 == 0 ? i : p1;
								pc2[nxt] = c2 == 0 ? j : p2;
								pcs[nxt] = cs == 0 ? (i + j + c) % 10 : ps;
							}						
						}
				}
		}
		StringBuilder x = new StringBuilder();
		StringBuilder y = new StringBuilder();
		StringBuilder z = new StringBuilder();
		int state = get(l1 + 1, l2 + 1, ls + 1, 0, 7);
		boolean t1 = true, t2 = true, ts = true;
		while(state != 0)
		{
			if(pc1[state] != 0 || !t1)
			{
				x.append(pc1[state]);
				t1 = false;
			}
			if(pc2[state] != 0 || !t2)
			{
				y.append(pc2[state]);
				t2 = false;
			}
			if(pcs[state] != 0 || !ts)
			{
				z.append(pcs[state]);
				ts = false;
			}
			state = p[state];
		}
		out.println(x.append("+").append(y).append("=").append(z));
		out.close();
	}

	static int m(int x, int y) { return Math.min(x, y); }

	static int get(int d1, int d2, int ds, int c, int cc) { return 5120 * cc + ((d1 * 8 + d2) * 8 + ds) * 10 + c; }

	static class Edge implements Comparable<Edge>
	{
		int state, cost;

		Edge(int a, int b) { state = a; cost = b; }

		public int compareTo(Edge e) { return cost - e.cost; }
	}

	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

		public Scanner(FileReader r){	br = new BufferedReader(r);}

		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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

		public String nextLine() throws IOException {return br.readLine();}

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

		public boolean ready() throws IOException {return br.ready();}


	}
}