58_E. Expression_5258
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
#include <bits/stdc++.h>
using namespace std;
const int N = 25;
int dp[N][N][N][N][2][2][2], na, nb, nc;
string a, b, c, A, B, C;
void pros(string &x) {
  reverse(x.begin(), x.end());
  x = ' ' + x;
}
struct col {
  int a, b, c;
} value[N][N][N][N][2][2][2];
struct pack {
  int i, posa, posb, posc, carry, enda, endb;
} trace[N][N][N][N][2][2][2], root;
int main(int argc, char const *argv[]) {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  string t, tmp;
  tmp.clear();
  cin >> t;
  for (int i = 0; i < t.size(); ++i) {
    if (t[i] >= '0' && t[i] <= '9') {
      tmp += t[i];
    } else {
      if (t[i] == '+') a = tmp;
      if (t[i] == '=') b = tmp;
      tmp.clear();
    }
  }
  c = tmp;
  na = a.size();
  nb = b.size();
  nc = c.size();
  pros(a);
  pros(b);
  pros(c);
  memset(dp, -1, sizeof dp);
  dp[0][0][0][0][0][0][0] = 0;
  int res = N * N;
  for (int i = 0; i <= 20; ++i)
    for (int posa = 0; posa <= na; ++posa)
      for (int posb = 0; posb <= nb; ++posb)
        for (int posc = 0; posc <= nc; ++posc)
          for (int carry = 0; carry <= 1; ++carry)
            for (int enda = 0; enda <= 1; ++enda)
              for (int endb = 0; endb <= 1; ++endb) {
                int cur = dp[i][posa][posb][posc][carry][enda][endb];
                pack address = {i, posa, posb, posc, carry, enda, endb};
                if (cur == -1) continue;
                for (int d1 = 0; d1 <= 9; ++d1)
                  for (int d2 = 0; d2 <= 9; ++d2) {
                    int s = d1 * (enda ? 0 : 1) + d2 * (endb ? 0 : 1) + carry;
                    int nxt = s % 10, ncarry = s / 10;
                    int pa = posa;
                    if (!enda && posa != na && a[posa + 1] - '0' == d1) pa++;
                    int pb = posb;
                    if (!endb && posb != nb && b[posb + 1] - '0' == d2) pb++;
                    int pc = posc;
                    if (posc != nc && c[posc + 1] - '0' == nxt) pc++;
                    for (int nea = enda; nea <= 1; ++nea)
                      for (int neb = endb; neb <= 1; ++neb) {
                        int &state = dp[i + 1][pa][pb][pc][ncarry][nea][neb];
                        if (state == -1 || state > cur + 3 - enda - endb) {
                          state = cur + 3 - enda - endb;
                          trace[i + 1][pa][pb][pc][ncarry][nea][neb] = address;
                          value[i + 1][pa][pb][pc][ncarry][nea][neb] = {
                              (enda ? -1 : d1), (endb ? -1 : d2), nxt};
                          continue;
                        }
                        state = min(state, cur + 3 - enda - endb);
                      }
                  }
                if (posa == na && posb == nb && posc == nc && res > cur &&
                    carry == 0) {
                  res = cur;
                  root = address;
                }
              }
  pack leaf = {0, 0, 0, 0, 0, 0, 0};
  while (root.i + root.posa + root.posb + root.posc + root.carry + root.enda +
             root.endb !=
         0) {
    col D = value[root.i][root.posa][root.posb][root.posc][root.carry]
                 [root.enda][root.endb];
    if (D.a != -1) A += char('0' + D.a);
    if (D.b != -1) B += char('0' + D.b);
    C += char('0' + D.c);
    root = trace[root.i][root.posa][root.posb][root.posc][root.carry][root.enda]
                [root.endb];
  }
  cout << A << "+" << B << "=" << C << endl;
  return 0;
}
