Problem:
Score : 600 points

Problem Statement

The squirrel Chokudai has N acorns.
One day, he decides to do some trades in multiple precious metal exchanges to make more acorns.

His plan is as follows:

Get out of the nest with N acorns in his hands.

Go to Exchange A and do some trades.

Go to Exchange B and do some trades.

Go to Exchange A and do some trades.

Go back to the nest.

In Exchange X (X = A, B), he can perform the following operations any integer number of times (possibly zero) in any order:

Lose g_{X} acorns and gain 1 gram of gold.

Gain g_{X} acorns and lose 1 gram of gold.

Lose s_{X} acorns and gain 1 gram of silver.

Gain s_{X} acorns and lose 1 gram of silver.

Lose b_{X} acorns and gain 1 gram of bronze.

Gain b_{X} acorns and lose 1 gram of bronze.

Naturally, he cannot perform an operation that would leave him with a negative amount of acorns, gold, silver, or bronze.

What is the maximum number of acorns that he can bring to the nest?
Note that gold, silver, or bronze brought to the nest would be worthless because he is just a squirrel.

Constraints

1 \leq N \leq 5000

1 \leq g_{X} \leq 5000

1 \leq s_{X} \leq 5000

1 \leq b_{X} \leq 5000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
g_A s_A b_A
g_B s_B b_B

Output

Print the maximum number of acorns that Chokudai can bring to the nest.

Sample Input 1

23
1 1 1
2 1 1

Sample Output 1

46

He can bring 46 acorns to the nest, as follows:

In Exchange A, trade 23 acorns for 23 grams of gold. {acorns, gold, silver, bronze}={ 0,23,0,0 }

In Exchange B, trade 23 grams of gold for 46 acorns. {acorns, gold, silver, bronze}={ 46,0,0,0 }

In Exchange A, trade nothing. {acorns, gold, silver, bronze}={ 46,0,0,0 }

He cannot have 47 or more acorns, so the answer is 46.

Solution in Rust (1.15.1) (judge verdict: Accepted)

/*------------------------------------------------------------------*/
/*------------------------- begin template -------------------------*/
/*------------------------------------------------------------------*/

// ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
// diff: using Parser
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut parser = Parser::from_str($s);
        input_inner!{parser, $($r)*}
    };
    (parser = $parser:ident, $($r:tt)*) => {
        input_inner!{$parser, $($r)*}
    };
    (new_stdin_parser = $parser:ident, $($r:tt)*) => {
        let stdin = std::io::stdin();
        let reader = std::io::BufReader::new(stdin.lock());
        let mut $parser = Parser::new(reader);
        input_inner!{$parser, $($r)*}
    };
    ($($r:tt)*) => {
        input!{new_stdin_parser = parser, $($r)*}
    };
}

macro_rules! input_inner {
    ($parser:ident) => {};
    ($parser:ident, ) => {};
    ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($parser, $t);
        input_inner!{$parser $($r)*}
    };
}

macro_rules! read_value {
    ($parser:ident, ( $($t:tt),* )) => {
        ( $(read_value!($parser, $t)),* )
    };
    ($parser:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
    };
    ($parser:ident, chars) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()
    };
    ($parser:ident, char_) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()[0]
    };
    ($parser:ident, usize1) => {
        read_value!($parser, usize) - 1
    };
    ($parser:ident, i64_) => {
        $parser.fast_i64()
    };
    ($parser:ident, usize_) => {
        $parser.fast_i64() as usize
    };
    ($parser:ident, usize1_) => {
        ($parser.fast_i64() - 1) as usize
    };
    ($parser:ident, $t:ty) => {
        $parser.next::<$t>().expect("Parse error")
    };
}

use std::io;
use std::io::BufRead;
use std::str;

// ref: tatsuya6502 <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e>
// ref: wariuni <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e#comment-7040a5ae96305e884eb9>
// diff: using std::io::BufRead::fill_buf()
pub struct Parser<R> {
    pub reader: R,
    buf: Vec<u8>,
    pos: usize,
}

impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}

impl<R: BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len, complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                (len, buf2[len - 1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.parse::<T>();
            } else {
                self.update_buf();
            }
        }
    }
    pub fn fast_i64(&mut self) -> i64 {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            if begin == self.buf.len() {
                self.update_buf();
                continue;
            }
            let mut res = 0;
            let (is_positive, mut end) = match self.buf[begin] {
                b'+' => (true, begin + 1),
                b'-' => (false, begin + 1),
                _ => (true, begin),
            };
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                res = res * 10 + (self.buf[end] as i64 - '0' as i64);
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return if is_positive { res } else { -res };
            } else {
                self.update_buf();
            }
        }
    }
}

#[allow(unused_imports)]
use std::cmp::*;

fn main() {
    input! {
        new_stdin_parser = parser,
    }
    let res = solve(&mut parser);
    print!("{}", res);
}

/*------------------------------------------------------------------*/
/*-------------------------- end template --------------------------*/
/*------------------------------------------------------------------*/

use std::fmt::Write;
fn solve<R: BufRead>(parser: &mut Parser<R>) -> String {
    let mut buf = String::new();
    input! {
        parser = parser,
        n: usize,
        xs: [usize; 3],
        ys: [usize; 3],
    }
    let g_min = min(xs[0], ys[0]);
    let g_max = max(xs[0], ys[0]);
    let s_min = min(xs[1], ys[1]);
    let s_max = max(xs[1], ys[1]);
    let b_min = min(xs[2], ys[2]);
    let b_max = max(xs[2], ys[2]);
    let mins = [g_min, s_min, b_min];
    let maxs = [g_max, s_max, b_max];

    let mut left = vec![];
    let mut right = vec![];
    for i in 0..3 {
        if xs[i] < ys[i] {
            left.push(i);
        }
        if xs[i] > ys[i] {
            right.push(i);
        }
    }

    if left.len() == 0 || right.len() == 0 {
        let mut res = 0;
        for b in 0..n + 1 {
            for s in 0..n + 1 {
                if b + s > n {
                    break;
                }
                let g = n - s - b;
                let mut gain = 0;
                let ts = vec![g, s, b];
                for i in 0..3 {
                    gain += ts[i] / mins[i] * maxs[i];
                    gain += ts[i] % mins[i];
                }
                res = max(res, gain);
            }
        }
        writeln!(buf, "{}", res);
    } else {
        let mid = if left.len() == 1 {
            n / mins[left[0]] * maxs[left[0]] + n % mins[left[0]]
        } else if left.len() == 2 {
            let (large_i, small_i) =
                if maxs[left[0]] * mins[left[1]] >= maxs[left[1]] * mins[left[0]] {
                    (left[0], left[1])
                } else {
                    (left[1], left[0])
                };
            let mut res = 0;
            let max_large_n = n / mins[large_i];
            let min_large_n = max(0, max_large_n as i64 - 7000) as usize;
            for large_n in min_large_n..max_large_n + 1 {
                let t_large = large_n * mins[large_i];
                let t_small = n - t_large;
                let s_large = t_large / mins[large_i] * maxs[large_i] + t_large % mins[large_i];
                let s_small = t_small / mins[small_i] * maxs[small_i] + t_small % mins[small_i];
                res = max(res, s_large + s_small);
            }
            res
        } else {
            panic!();
        };
        let n = mid;
        let left = right;
        let res = if left.len() == 1 {
            n / mins[left[0]] * maxs[left[0]] + n % mins[left[0]]
        } else if left.len() == 2 {
            let (large_i, small_i) =
                if maxs[left[0]] * mins[left[1]] >= maxs[left[1]] * mins[left[0]] {
                    (left[0], left[1])
                } else {
                    (left[1], left[0])
                };
            let mut res = 0;
            let max_large_n = n / mins[large_i];
            let min_large_n = max(0, max_large_n as i64 - 7000) as usize;
            for large_n in min_large_n..max_large_n + 1 {
                let t_large = large_n * mins[large_i];
                let t_small = n - t_large;
                let s_large = t_large / mins[large_i] * maxs[large_i] + t_large % mins[large_i];
                let s_small = t_small / mins[small_i] * maxs[small_i] + t_small % mins[small_i];
                res = max(res, s_large + s_small);
            }
            res
        } else {
            panic!();
        };
        writeln!(buf, "{}", res);
    }
    buf
}