Three teammates take part in a well-known programming contest. They want to solve one problem as fast as possible. First, someone must read the problem. For each teammate, we know how much time they need to read it. Then someone must come up with a solution. For each teammate, we know how much time they need for this. But if this is not the person who read the problem, the reader needs extra time to explain the statement to them. The last step is writing the code. Again, for each teammate, we know how much time they need. But if the code is written by someone else, not by the person who came up with the solution, the author of the idea needs time to explain the solution to the one who writes the code.

Using all this information, find the minimum time in which the team can submit the problem. Assume that the judging system works instantly and no debugging is needed after the submission

The first line contains 3 integers x₁, x₂, x₃ (1 ≤ x₁, x₂, x₃ ≤ 10⁹) — the time each teammate needs to read the problem.

The second line contains 3 integers y₁, y₂, y₃ (1 ≤ y₁, y₂, y₃ ≤ 10⁹) — the time each teammate needs to come up with the solution.

The third line contains 3 integers z₁, z₂, z₃ (1 ≤ z₁, z₂, z₃ ≤ 10⁹) — the time each teammate needs to write the code.

The next 3 lines contain 3 integers each — matrix b (0 ≤ b_ij ≤ 10⁹, 1 ≤ i, j ≤ 3). b_ij denotes the time needed for teammate i to explain the statement to teammate j. It is guaranteed that b_ii = 0 for all 1 ≤ i ≤ 3, and also b_ij > 0 for all 1 ≤ i, j ≤ 3, i ≠q j.

The next 3 lines contain 3 integers each — matrix c (0 ≤ c_ij ≤ 10⁹, 1 ≤ i, j ≤ 3). c_ij denotes the time needed for teammate i to explain the solution to teammate j. It is guaranteed that c_ii = 0 for all 1 ≤ i ≤ 3, and also c_ij > 0 for all 1 ≤ i, j ≤ 3, i ≠q j.

Print a single integer — the answer to the problem.