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Given are three arrays of $n+1$ integers: $a$, $b$, $c$.

We define $3n+1$ functions $F_0, F_1, \ldots, F_{3n}$ as follows:

$$F_i(t) = it + \max\limits_{\substack{0 \leq x, y, z \leq n \\ x + y + z = i}} {(a_x + b_y + c_z)}\text{.}$$

A function $F_i$ is said to be NeVeR\_LosEs if and only if there does not exist a real number $t$ such that $F_i(t)>F_j(t)$ for all $j \neq i$.

Your task is to find out which functions can be called NeVeR\_LosEs.

The first line contains an integer $n$ ($1 \leq n \leq 3 \cdot 10^5$).

The second line contains the array $a_0, a_1, \ldots, a_n$ ($0 \leq a_i \leq 10^9$).

The third line contains the array $b_0, b_1, \ldots, b_n$ ($0 \leq b_i \leq 10^9$).

The fourth line contains the array $c_0, c_1, \ldots, c_n$ ($0 \leq c_i \leq 10^9$).

On the first line, print an integer $m$, the number of functions that can be called NeVeR\_LosEs.

On the second line, print $m$ integers $0 \leq i_1 \leq \ldots \leq i_m \leq 3n$, the indices of these functions in ascending order.