Burger Making

Problem Description

A burger recipe is a string made of characters B, S, C, indicating the ingredients needed for a burger from bottom to top: B for bread, S for sausage, and C for cheese. A burger must be made exactly according to the recipe's ingredient counts — not one more, not one less.

The kitchen currently has $b$ pieces of bread, $s$ sausages, and $c$ pieces of cheese. If ingredients are insufficient, you can buy them at the supermarket: each piece of bread costs $B$ yuan, each sausage costs $S$ yuan, and each piece of cheese costs $C$ yuan. You have $money$ yuan in total.

Find the maximum number of burgers you can make.

Input Format

The first line contains a string $s$, the recipe.

The second line contains three integers $b, s, c$, the current ingredient counts in the kitchen.

The third line contains three integers $B, S, C$, the unit prices of the three ingredients at the supermarket.

The fourth line contains an integer $money$, the amount of money available.

Output Format

Output one integer, the maximum number of burgers that can be made.

Sample Input

BBBSSC
6 4 1
1 2 3
4

Sample Output

2

Constraints

• $|s|\le 100$
• $0\le b,s,c\le 100$
• $0\le B,S,C\le 100$
• $0\le money\le 10^{12}$