Problem:
Score : 600 points

Problem Statement

We have N strings of lowercase English letters: S_1, S_2, \cdots, S_N.

Takahashi wants to make a string that is a palindrome by choosing one or more of these strings - the same string can be chosen more than once - and concatenating them in some order of his choice.

The cost of using the string S_i once is C_i, and the cost of using it multiple times is C_i multiplied by that number of times.

Find the minimum total cost needed to choose strings so that Takahashi can make a palindrome.

If there is no choice of strings in which he can make a palindrome, print -1.

Constraints

1 \leq N \leq 50

1 \leq |S_i| \leq 20

S_i consists of lowercase English letters.

1 \leq C_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
S_1 C_1
S_2 C_2
:
S_N C_N

Output

Print the minimum total cost needed to choose strings so that Takahashi can make a palindrome, or -1 if there is no such choice.

Sample Input 1

3
ba 3
abc 4
cbaa 5

Sample Output 1

7

We have ba, abc, and cbaa.

For example, we can use ba once and abc once for a cost of 7, then concatenate them in the order abc, ba to make a palindrome.
Also, we can use abc once and cbaa once for a cost of 9, then concatenate them in the order cbaa, abc to make a palindrome.

We cannot make a palindrome for a cost less than 7, so we should print 7.

Sample Input 2

2
abcab 5
cba 3

Sample Output 2

11

We can choose abcab once and cba twice, then concatenate them in the order abcab, cba, cba to make a palindrome for a cost of 11.

Sample Input 3

4
ab 5
cba 3
a 12
ab 10

Sample Output 3

8

We can choose a once, which is already a palindrome, but it is cheaper to concatenate ab and cba.

Sample Input 4

2
abc 1
ab 2

Sample Output 4

-1

We cannot make a palindrome, so we should print -1.

Solution in Rust (1.42.0) (judge verdict: Wrong Answer)

#![allow(unused_imports)]
#![allow(non_snake_case, unused)]

use std::cmp::*;
use std::collections::*;
use std::ops::*;

// https://atcoder.jp/contests/hokudai-hitachi2019-1/submissions/10518254

macro_rules! eprint {
    ($($t:tt)*) => {{
        use ::std::io::Write;
        let _ = write!(::std::io::stderr(), $($t)*);
    }};
}
macro_rules! eprintln {
    () => { eprintln!(""); };
    ($($t:tt)*) => {{
        use ::std::io::Write;
        let _ = writeln!(::std::io::stderr(), $($t)*);
    }};
}
macro_rules! dbg {
    ($v:expr) => {{
        let val = $v;
        eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($v), val);
        val
    }}
}

macro_rules! mat {
    ($($e:expr),*) => { Vec::from(vec![$($e),*]) };
    ($($e:expr,)*) => { Vec::from(vec![$($e),*]) };
    ($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) };
    ($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) };
}

macro_rules! ok {
    ($a:ident$([$i:expr])*.$f:ident()$(@$t:ident)*) => {
        $a$([$i])*.$f($($t),*)
    };
    ($a:ident$([$i:expr])*.$f:ident($e:expr$(,$es:expr)*)$(@$t:ident)*) => { {
        let t = $e;
        ok!($a$([$i])*.$f($($es),*)$(@$t)*@t)
    } };
}

pub fn readln() -> String {
    let mut line = String::new();
    ::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e));
    line
}

macro_rules! read {
    ($($t:tt),*; $n:expr) => {{
        let stdin = ::std::io::stdin();
        let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| {
            let line = line.unwrap();
            let mut it = line.split_whitespace();
            _read!(it; $($t),*)
        }).collect::<Vec<_>>();
        ret
    }};
    ($($t:tt),*) => {{
        let line = readln();
        let mut it = line.split_whitespace();
        _read!(it; $($t),*)
    }};
}

macro_rules! _read {
    ($it:ident; [char]) => {
        _read!($it; String).chars().collect::<Vec<_>>()
    };
    ($it:ident; [u8]) => {
        Vec::from(_read!($it; String).into_bytes())
    };
    ($it:ident; usize1) => {
        $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1
    };
    ($it:ident; [usize1]) => {
        $it.map(|s| s.parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::<Vec<_>>()
    };
    ($it:ident; [$t:ty]) => {
        $it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::<Vec<_>>()
    };
    ($it:ident; $t:ty) => {
        $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e))
    };
    ($it:ident; $($t:tt),+) => {
        ($(_read!($it; $t)),*)
    };
}


pub fn main() {
    let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join();
}

const MOD: usize = 1_000_000_007;
const INF: i64 = std::i64::MAX/2;

const TIME_LIMIT: f64 = 1.8;
 
fn get_time() -> f64 {
	static mut STIME: f64 = -1.0;
	let t = std::time::SystemTime::now().duration_since(std::time::UNIX_EPOCH).unwrap();
	let ms = t.as_secs() as f64 + t.subsec_nanos() as f64 * 1e-9;
	unsafe {
		if STIME < 0.0 {
			STIME = ms;
		}
		ms - STIME
	}
}

fn solve() {
    let n = read!(usize);
    let sc = read!([char],i64;n);
    let mut slist = vec![];
    let mut clist = vec![];
    for (a,b) in sc {
        slist.push(a);
        clist.push(b);
    }
    let mut count = vec![0;n];
    let ans = dfs(&slist,&clist,vec![],vec![],0,0,&mut count);
    println!("{}",if ans==INF {-1} else {ans});
}

fn dfs(slist: &Vec<Vec<char>>, clist: &Vec<i64>, head: Vec<char>, tail: Vec<char>, cost: i64, depth: i64, mut count: &mut Vec<i64>) -> i64 {
    if depth==200 {
        return INF;
    }
    for i in 0..count.len() {
        if count[i]>=20 {
            return INF;
        }
    }
    if get_time() > TIME_LIMIT {
        return INF;
    }
    let mut nc = VecDeque::new();
    for &h in &head {
        nc.push_back(h);
    }
    for i in (0..tail.len()).rev() {
        nc.push_back(tail[i]);
    }
    let mut flag = true;
    while !nc.is_empty() {
        let a = nc.pop_front();
        if nc.is_empty() {
            break;
        }
        let b = nc.pop_back();
        if a!=b {
            flag = false;
            break;
        }
    }
    if flag && !(head.is_empty()&&tail.is_empty()){
        return cost;
    }
    let mut ret = INF;
    if head.len()==tail.len() && !head.is_empty(){
        return INF;
    }
    if head.len() > tail.len() {
        for (id,s) in slist.iter().enumerate() {
            // println!("{:?} {:?} {:?}",head,tail,s);
            let mut flag = true;
            for i in 0..s.len() {
                if tail.len()+i >= head.len() {
                    break;
                }
                if s[s.len()-1-i] != head[tail.len()+i] {
                    flag = false;
                }
            }
            if !flag {
                continue;
            }
            let mut ntail = tail.clone();
            for i in (0..s.len()).rev() {
                ntail.push(s[i]);
            }
            count[id] += 1;
            ret = min(ret, dfs(&slist,&clist,head.clone(),ntail,cost+clist[id],depth+1,&mut count));
        }
    }
    else {
        for (id,s) in slist.iter().enumerate() {
            let mut flag = true;
            for i in 0..s.len() {
                if head.len()+i >= tail.len() {
                    break;
                }
                if s[i] != tail[head.len()+i] {
                    flag = false;
                }
            }
            if !flag {
                continue;
            }
            let mut nhead = head.clone();
            for i in 0..s.len() {
                nhead.push(s[i]);
            }
            count[id] += 1;
            ret = min(ret, dfs(&slist,&clist,nhead,tail.clone(),cost+clist[id],depth+1,&mut count));
        }
    }
    return ret;
}

fn run() {
    solve();
}