Problem:
Score : 300 points

Problem Statement

Joisino is planning to open a shop in a shopping street.

Each of the five weekdays is divided into two periods, the morning and the evening. For each of those ten periods, a shop must be either open during the whole period, or closed during the whole period. Naturally, a shop must be open during at least one of those periods.

There are already N stores in the street, numbered 1 through N.

You are given information of the business hours of those shops, F_{i,j,k}. If F_{i,j,k}=1, Shop i is open during Period k on Day j (this notation is explained below); if F_{i,j,k}=0, Shop i is closed during that period. Here, the days of the week are denoted as follows. Monday: Day 1, Tuesday: Day 2, Wednesday: Day 3, Thursday: Day 4, Friday: Day 5. Also, the morning is denoted as Period 1, and the afternoon is denoted as Period 2.

Let c_i be the number of periods during which both Shop i and Joisino's shop are open. Then, the profit of Joisino's shop will be P_{1,c_1}+P_{2,c_2}+...+P_{N,c_N}.

Find the maximum possible profit of Joisino's shop when she decides whether her shop is open during each period, making sure that it is open during at least one period.

Constraints

1≤N≤100

0≤F_{i,j,k}≤1

For every integer i such that 1≤i≤N, there exists at least one pair (j,k) such that F_{i,j,k}=1.

-10^7≤P_{i,j}≤10^7

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
F_{1,1,1} F_{1,1,2} ... F_{1,5,1} F_{1,5,2}
:
F_{N,1,1} F_{N,1,2} ... F_{N,5,1} F_{N,5,2}
P_{1,0} ... P_{1,10}
:
P_{N,0} ... P_{N,10}

Output

Print the maximum possible profit of Joisino's shop.

Sample Input 1

1
1 1 0 1 0 0 0 1 0 1
3 4 5 6 7 8 9 -2 -3 4 -2

Sample Output 1

8

If her shop is open only during the periods when Shop 1 is opened, the profit will be 8, which is the maximum possible profit.

Sample Input 2

2
1 1 1 1 1 0 0 0 0 0
0 0 0 0 0 1 1 1 1 1
0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1
0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1

Sample Output 2

-2

Note that a shop must be open during at least one period, and the profit may be negative.

Sample Input 3

3
1 1 1 1 1 1 0 0 1 1
0 1 0 1 1 1 1 0 1 0
1 0 1 1 0 1 0 1 0 1
-8 6 -2 -8 -8 4 8 7 -6 2 2
-9 2 0 1 7 -5 0 -2 -6 5 5
6 -6 7 -9 6 -5 8 0 -9 -7 -7

Sample Output 3

23

Solution in Rust (1.42.0) (judge verdict: Accepted)

// -*- coding:utf-8-unix -*-

extern crate lazy_static;
extern crate num_bigint;
// 0.2.2
extern crate num_traits;

// 0.2.8
use num_bigint::BigInt;
use num_traits::{one, zero, Num, NumAssignOps, NumOps, One, Pow, Zero};

// use proconio::derive_readable;
use proconio::fastout;
use proconio::input;
// use std::convert::TryInto;
use itertools::{assert_equal, concat};
use lazy_static::lazy_static;
// use libm::*;
use std::cmp::*;
use std::collections::{BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::*;
use std::mem::swap;
use std::ops::{BitAnd, Range, ShrAssign};
use std::str::FromStr;
use std::sync::Mutex;
use superslice::*;

// ##########
// read
// ###########
pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

// ##########
// chmin, chmax
// https://qiita.com/maguro_tuna/items/fab200fdc1efde1612e7
// ###########

#[allow(unused_macros)]
macro_rules! chmin {
    ($base:expr, $($cmps:expr),+ $(,)*) => {{
        let cmp_min = min!($($cmps),+);
        if $base > cmp_min {
            $base = cmp_min;
            true
        } else {
            false
        }
    }};
}

#[allow(unused_macros)]
macro_rules! chmax {
    ($base:expr, $($cmps:expr),+ $(,)*) => {{
        let cmp_max = max!($($cmps),+);
        if $base < cmp_max {
            $base = cmp_max;
            true
        } else {
            false
        }
    }};
}

#[allow(unused_macros)]
macro_rules! min {
    ($a:expr $(,)*) => {{
        $a
    }};
    ($a:expr, $b:expr $(,)*) => {{
        std::cmp::min($a, $b)
    }};
    ($a:expr, $($rest:expr),+ $(,)*) => {{
        std::cmp::min($a, min!($($rest),+))
    }};
}

#[allow(unused_macros)]
macro_rules! max {
    ($a:expr $(,)*) => {{
        $a
    }};
    ($a:expr, $b:expr $(,)*) => {{
        std::cmp::max($a, $b)
    }};
    ($a:expr, $($rest:expr),+ $(,)*) => {{
        std::cmp::max($a, max!($($rest),+))
    }};
}

// ##########
// lazy_static!
// ##########
// lazy_static! {
//     static ref H: Mutex<Vec<i32>> = Mutex::default();
//     static ref W: Mutex<Vec<i32>> = Mutex::default();
// }
// let mut values = VALUES.lock().unwrap();
// values.extend_from_slice(&[1, 2, 3, 4]);
// assert_eq!(&*values, &[1, 2, 3, 4]);

// const MOD: usize = 1000_000_000 + 7;

// ##########
// modint
// https://qiita.com/drken/items/3b4fdf0a78e7a138cd9a
// ##########

#[allow(dead_code)]
fn modinv<T: Num + NumAssignOps + NumOps + Copy + PartialOrd>(a: T, m: T) -> T {
    let mut a = a;
    let mut b = m;
    let mut u: T = one();
    let mut v: T = zero();

    while b != zero() {
        let t = a / b;
        a -= t * b;
        swap(&mut a, &mut b);
        u -= t * v;
        swap(&mut u, &mut v);
    }
    u %= m;
    if u < zero() {
        u += m;
    }
    return u;
}

#[test]
fn modinv_test() {
    assert_eq!(1, modinv(1, 13));
    assert_eq!(2, modinv(7, 13));
    assert_eq!(3, modinv(9, 13));
    assert_eq!(4, modinv(10, 13));
    assert_eq!(5, modinv(8, 13));
}

// long long modpow(long long a, long long n, long long mod) {
// long long res = 1;
// while (n > 0) {
// if (n & 1) res = res * a % mod;
// a = a * a % mod;
// n >>= 1;
// }
// return res;
// }
#[allow(dead_code)]
fn modpow<T>(a: T, n: T, modulo: T) -> T
where
    T: Num + NumAssignOps + NumOps + Copy + PartialOrd + BitAnd + PartialEq + ShrAssign,
    <T as BitAnd>::Output: PartialEq + Num,
{
    let mut res = one();
    let mut a = a;
    let mut n = n;
    while n > zero() {
        if (n & one()) == one() {
            res = res * a % modulo;
        }
        a = a * a % modulo;
        n >>= one();
    }

    return res;
}

#[test]
fn modpow_test() {
    assert_eq!(4, modpow(2, 2, 13));
    assert_eq!(3, modpow(2, 4, 13));
}

// 前処理 com_init(): O(n)
// クエリ処理 COM(n, k): O(1)
// conv::com_init();
// conv::com(n,k);
mod comb {
    use super::*;
    lazy_static! {
        static ref FAC: Mutex<Vec<usize>> = Mutex::default();
        static ref FINV: Mutex<Vec<usize>> = Mutex::default();
        static ref INV: Mutex<Vec<usize>> = Mutex::default();
        static ref MODULO: Mutex<usize> = Mutex::default();
        // static ref MAXNCONV: Mutex<usize> = Mutex::default();
    }

    // // テーブルを作る前処理
    // void com_init() {
    // fac[0] = fac[1] = 1;
    // finv[0] = finv[1] = 1;
    // inv[1] = 1;
    // for (int i = 2; i < MAX; i++){
    // fac[i] = fac[i - 1] * i % MOD;
    // inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
    // finv[i] = finv[i - 1] * inv[i] % MOD;
    // }

    #[allow(dead_code)]
    fn com_init_with(modulo: usize, maxn_conv: usize) {
        let mut fac = FAC.lock().unwrap();
        let mut finv = FINV.lock().unwrap();
        let mut inv = INV.lock().unwrap();
        *fac = vec![0; maxn_conv];
        *finv = vec![0; maxn_conv];
        *inv = vec![0; maxn_conv];

        let mut g_modulo = MODULO.lock().unwrap();
        *g_modulo = modulo;

        fac[0] = 1;
        fac[1] = 1;
        finv[0] = 1;
        finv[1] = 1;
        inv[1] = 1;

        for i in 2..maxn_conv {
            fac[i] = fac[i - 1] * i % modulo;
            inv[i] = modulo - inv[modulo % i] * (modulo / i) % modulo;
            finv[i] = finv[i - 1] * inv[i] % modulo;
        }
    }

    #[allow(dead_code)]
    pub fn com_init() {
        com_init_with(MOD, MAXN_CONV);
    }

    // // 二項係数計算
    // long long COM(int n, int k){
    // if (n < k) return 0;
    // if (n < 0 || k < 0) return 0;
    // return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
    // }
    #[allow(dead_code)]
    pub fn com(n: usize, k: usize) -> usize {
        let fac = FAC.lock().unwrap();
        let finv = FINV.lock().unwrap();
        // let mut inv = INV.lock().unwrap();
        let m = *MODULO.lock().unwrap();

        if n < k {
            return 0;
        }
        // if n < 0 || k < 0 {
        //     return 0;
        // }
        return fac[n] * (finv[k] * finv[n - k] % m) % m;
    }

    #[test]
    fn com_test() {
        com_init_with(13, 100);
        assert_eq!(12, com(12, 1));
        assert_eq!(66 % 13, com(12, 2));
        assert_eq!(220 % 13, com(12, 3));
        assert_eq!(495 % 13, com(12, 4));
        assert_eq!(792 % 13, com(12, 5));
        assert_eq!(924 % 13, com(12, 6));
        assert_eq!(com(12, 5), com(12, 7));
    }
}

// ##########
// union-find
// http://sntea.hatenablog.com/entry/2017/06/07/091246
// ##########

mod uf {
    // let mut uf = uf::UnionFind::new(10);
    // uf.unite; uf.same
    #[allow(dead_code)]
    struct UnionFind {
        par: Vec<usize>,
        rank: Vec<usize>,
    }

    impl UnionFind {
        #[allow(dead_code)]
        pub fn new(n: usize) -> UnionFind {
            let mut vec = vec![0; n];
            for i in 0..n {
                vec[i] = i;
            }
            UnionFind {
                par: vec,
                rank: vec![0; n],
            }
        }

        #[allow(dead_code)]
        fn find(&mut self, x: usize) -> usize {
            if x == self.par[x] {
                x
            } else {
                let par = self.par[x];
                let res = self.find(par);
                self.par[x] = res;
                res
            }
        }

        #[allow(dead_code)]
        pub fn same(&mut self, a: usize, b: usize) -> bool {
            self.find(a) == self.find(b)
        }

        #[allow(dead_code)]
        pub fn unite(&mut self, a: usize, b: usize) {
            let apar = self.find(a);
            let bpar = self.find(b);
            if self.rank[apar] > self.rank[bpar] {
                self.par[bpar] = apar;
            } else {
                self.par[apar] = bpar;
                if self.rank[apar] == self.rank[bpar] {
                    self.rank[bpar] += 1;
                }
            }
        }
    }

    #[test]
    fn union_find_test() {
        let mut uf = UnionFind::new(10);

        for i in 0..10 {
            for j in 0..10 {
                assert_eq!(i == j, uf.same(i, j));
            }
        }

        uf.unite(0, 1);
        assert_eq!(true, uf.same(0, 1));
        //false
        assert_eq!(false, uf.same(0, 9));
        assert_eq!(false, uf.same(1, 9));
        assert_eq!(false, uf.same(2, 9));

        uf.unite(8, 9);
        assert_eq!(true, uf.same(0, 1));
        assert_eq!(true, uf.same(8, 9));
        //false
        assert_eq!(false, uf.same(0, 9));
        assert_eq!(false, uf.same(1, 9));
        assert_eq!(false, uf.same(2, 9));

        uf.unite(1, 9);
        assert_eq!(true, uf.same(0, 1));
        assert_eq!(true, uf.same(8, 9));
        assert_eq!(true, uf.same(0, 8));
        assert_eq!(true, uf.same(0, 9));
        assert_eq!(true, uf.same(1, 8));
        assert_eq!(true, uf.same(1, 9));
        //false
        assert_eq!(false, uf.same(2, 9));
    }
}

// ###########
// seg_tree
// ant_book
// ###########
mod seg_tree {
    #[derive(Debug)]
    struct SegTree<T: Clone> {
        n: usize,
        dat: Vec<Option<T>>,
    }

    impl<T: Clone + std::fmt::Debug> SegTree<T> {
        #[allow(dead_code)]
        pub fn new(size: usize) -> SegTree<T> {
            let mut size_pow2 = 1;
            while size_pow2 < size {
                size_pow2 *= 2;
            }

            let dat: Vec<Option<T>> = vec![None; 2 * size_pow2 - 1];
            SegTree { n: size_pow2, dat }
        }

        #[allow(dead_code)]
        pub fn update<F: Fn(&Option<T>, &Option<T>) -> Option<T>>(
            &mut self,
            k: usize,
            a: T,
            update: F,
        ) {
            let mut k = k;
            k += self.n - 1;
            self.dat[k] = Some(a);
            while k > 0 {
                k = (k - 1) / 2;
                self.dat[k] = update(&self.dat[k * 2 + 1], &self.dat[k * 2 + 2]);
            }
        }

        #[allow(dead_code)]
        fn query_inner<F: Fn(&Option<T>, &Option<T>) -> Option<T>>(
            &self,
            selection_query: &F,
            a: usize,
            b: usize,
            k: usize,
            l: usize,
            r: usize,
        ) -> Option<T> {
            if r <= a || b <= l {
                // eprintln!("{}, {}, {}, {}, {:?}", a, b, l, r, "none");
                return None;
            }

            return if a <= l && r <= b {
                // eprintln!("{}, {}, {}, {}, {:?}", a, b, r, l, self.dat[k]);
                self.dat[k].clone()
            } else {
                let vl = self.query_inner(selection_query, a, b, k * 2 + 1, l, (l + r) / 2);
                let vr = self.query_inner(selection_query, a, b, k * 2 + 2, (l + r) / 2, r);

                selection_query(&vl, &vr)
            };
        }

        #[allow(dead_code)]
        pub fn query<F: Fn(&Option<T>, &Option<T>) -> Option<T>>(
            &self,
            selection_query: &F,
            a: usize,
            b: usize,
        ) -> Option<T> {
            return self.query_inner(selection_query, a, b, 0, 0, self.n);
        }
    }

    #[test]
    fn test_segtree_rmq() {
        let mut t: SegTree<usize> = SegTree::new(5);

        let cmp_f = |lhs: &Option<usize>, rhs: &Option<usize>| {
            if lhs.is_none() {
                return rhs.clone();
            }

            if rhs.is_none() {
                return lhs.clone();
            }

            return if lhs.unwrap() <= rhs.unwrap() {
                lhs.clone()
            } else {
                rhs.clone()
            };
        };
        // 1, 3, 2, 5, 1
        t.update(0, 1, cmp_f);
        t.update(1, 3, cmp_f);
        t.update(2, 2, cmp_f);
        t.update(3, 5, cmp_f);
        t.update(4, 1, cmp_f);
        // println!("{:?}", t);

        assert_eq!(1, t.query(&cmp_f, 0, 1).unwrap());
        assert_eq!(3, t.query(&cmp_f, 1, 2).unwrap());
        assert_eq!(2, t.query(&cmp_f, 2, 3).unwrap());
        assert_eq!(5, t.query(&cmp_f, 3, 4).unwrap());
        assert_eq!(1, t.query(&cmp_f, 4, 5).unwrap());

        // len2
        assert_eq!(1, t.query(&cmp_f, 0, 2).unwrap());
        assert_eq!(2, t.query(&cmp_f, 1, 3).unwrap());
        assert_eq!(2, t.query(&cmp_f, 2, 4).unwrap());
        assert_eq!(1, t.query(&cmp_f, 3, 5).unwrap());

        // len3
        assert_eq!(1, t.query(&cmp_f, 0, 3).unwrap());
        assert_eq!(2, t.query(&cmp_f, 1, 4).unwrap());
        assert_eq!(1, t.query(&cmp_f, 2, 5).unwrap());

        // len4
        assert_eq!(1, t.query(&cmp_f, 0, 4).unwrap());
        assert_eq!(1, t.query(&cmp_f, 1, 5).unwrap());

        // len5
        assert_eq!(1, t.query(&cmp_f, 0, 6).unwrap());
    }
}

// let mut values = VALUES.lock().unwrap();
// values.extend_from_slice(&[1, 2, 3, 4]);

// MOD, Combination関連に使う定数
#[allow(dead_code)]
const MOD: usize = 1000000007;
#[allow(dead_code)]
const MAXN_CONV: usize = 510000;

// abc080-C
// #[fastout]
fn main() {
    const TIMES: usize = 10;

    input![n: usize, f: [[i8; TIMES]; n], p: [[i64; TIMES + 1]; n]];
    // eprintln!("{:?}", f);
    // eprintln!("{:?}", p);

    let mut ans = std::i64::MIN / 2;
    for i in 1..2usize.pow(TIMES as u32) {
        let mut opens = vec![false; TIMES];

        let mut idx = 0;
        let mut i = i;
        while i > 0 {
            if i & 1 == 1 {
                opens[idx] = true;
            }

            i >>= 1;
            idx += 1;
        }

        let mut cand: i64 = 0;

        for i in 0..n {
            let same_open: usize = f[i]
                .iter()
                .zip(opens.iter())
                .map(|(b1, b2)| if (*b1 == 1) && *b2 { 1 } else { 0 })
                .sum();

            // eprintln!(
            //     "{}, {:?}, {}, {}, {}",
            //     cand, opens, i, same_open, p[i][same_open]
            // );
            cand += p[i][same_open];
        }

        chmax!(ans, cand);
    }

    println!("{}", ans);
}