Ecosystem Energy Chain

In an ecosystem there are n+2 species numbered from 0 to n+1. Species 0 is the producer which supplies a fixed amount of energy, and species n+1 is the top predator (you) that can prey upon any species. For each species i with 1 ≤ i ≤ n, it is a predator that has a prey preference: it can only prey on species with indices in the range [0, r_i]. It is guaranteed that for every i (1 ≤ i ≤ n) the condition r_i < i holds and the sequence r₁, r₂, …, r_n is non‐decreasing (i.e. r_i ≤ r_i+1 for 1 ≤ i < n).

Each species i (0 ≤ i ≤ n) captures an amount of energy b_i. In order to survive, species i requires at least a_i units of energy, i.e. b_i ≥ a_i. In addition, an organism may pass some of its captured energy to its predators. However, the total energy transferred from species i cannot exceed ⅕ b_i (i.e. at most 20% efficiency): $$\text{transferred energy } c_i \le \frac{1}{5} b_i. $$

In the optimal scenario we assume every species uses its full transmission capacity. Thus, for species i (0 ≤ i ≤ n) we have

$$b_i = a_i + \frac{1}{5} b_i,$$

which implies

$$b_i = \frac{5}{4} a_i \quad \text{and} \quad f_i = \frac{1}{5}b_i = \frac{a_i}{4}, $$

where f_i is the maximum extra energy that species i can forward. However, for species i (1 ≤ i ≤ n) the available extra energy is also limited by what they can obtain from their allowed prey. Formally, let F_i denote the actual forwarded energy from species i, then:

• For the producer (i=0): $$ F_0 = \frac{a_0}{4}. $$
• For each species i (1 ≤ i ≤ n): $$ F_i = \min\Biggl(\sum_{j=0}^{r_i} F_j,\; \frac{a_i}{4}\Biggr). $$

The top predator (species n+1) can prey on every species. Therefore, the maximum energy you can obtain is the sum of all the forwarded energies from species 0 to n:

$$\text{Answer} = \sum_{i=0}^{n} F_i.$$

Given the minimum energy requirements a₀, a₁, …, a_n and the prey restrictions r₁, r₂, …, r_n, calculate the maximum energy the top predator (species n+1) can acquire, under the condition that all species survive.

inputFormat

The input consists of three lines:

1. The first line contains a single integer n (1 ≤ n).
2. The second line contains n+1 space‑separated integers: a₀, a₁, …, a_n, where a_i is the minimum energy required by species i (0 ≤ i ≤ n).
3. The third line contains n space‑separated integers: r₁, r₂, …, r_n, representing the maximum index of species that species i (1 ≤ i ≤ n) can prey on. It is guaranteed that for each 1 ≤ i ≤ n, r_i < i and r_i ≤ r_i+1 for 1 ≤ i < n.

outputFormat

Output a single number: the maximum energy the top predator (species n+1) can obtain. The result should be printed with exactly 6 decimal places.

sample

1
4 5
0

2.000000