This is the easy version of the problem. The only difference is that in this version q=1. You can make hacks only if all versions of the problem are solved.

Zookeeper has been teaching his q sheep how to write and how to add. The i-th sheep has to write exactly k non-negative integers with the sum n_i.

Strangely, sheep have superstitions about digits and believe that the digits 3, 6, and 9 are lucky. To them, the fortune of a number depends on the decimal representation of the number; the fortune of a number is equal to the sum of fortunes of its digits, and the fortune of a digit depends on its value and position and can be described by the following table. For example, the number 319 has fortune F_{2} + 3F_{0}. 

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Each sheep wants to maximize the sum of fortune among all its k written integers. Can you help them?

Input

The first line contains a single integer k (1 ≤ k ≤ 999999): the number of numbers each sheep has to write. 

The next line contains six integers F_0, F_1, F_2, F_3, F_4, F_5 (1 ≤ F_i ≤ 10^9): the fortune assigned to each digit. 

The next line contains a single integer q (q = 1): the number of sheep.

Each of the next q lines contains a single integer n_i (1 ≤ n_i ≤ 999999): the sum of numbers that i-th sheep has to write. In this version, there is only one line.

Output

Print q lines, where the i-th line contains the maximum sum of fortune of all numbers of the i-th sheep. In this version, you should print only one line.

Examples

Input


3
1 2 3 4 5 6
1
57


Output


11

Input


3
1 2 3 4 5 6
1
63


Output


8

Note

In the first test case, 57 = 9 + 9 + 39. The three 9's contribute 1 ⋅ 3 and 3 at the tens position contributes 2 ⋅ 1. Hence the sum of fortune is 11.

In the second test case, 63 = 35 + 19 + 9. The sum of fortune is 8.

Source: codeforces | Difficulty: VERY_HARD
Tags: Dynamic programming

Greedy algorithms


Solutions: