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: Accepted)

#![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;

fn solve() {
    let n = read!(usize);
    let sc = read!(String,i64;n);
    let mut slist = vec![];
    let mut clist = vec![];
    for (s,c) in sc {
        slist.push(s);
        clist.push(c);
    }

    let mut map: HashMap<(String,String,bool,bool),i64> = HashMap::new();
    let mut q = BinaryHeap::new();
    q.push(Reverse((0,(String::new(),String::new(),false,true))));
    while let Some(Reverse(cur)) = q.pop() {
        let d = cur.0;
        let e = cur.1;
        let head = e.0.clone();
        let tail = e.1.clone();
        let h = e.0.chars().collect::<Vec<char>>();
        let t = e.1.chars().collect::<Vec<char>>();
        for (id,s) in slist.iter().enumerate() {
            let mut nhead = head.clone();
            let mut ntail = tail.clone();
            if nhead.len()==0 {
                nhead += s;
            }
            else {
                ntail += s;
            }
            let mut ret = judge(nhead, ntail);
            if !ret.3 {
                continue;
            }
            let cost = d + clist[id];
            let mut val = *map.get(&ret).unwrap_or(&INF);
            if val <= cost {
                continue;
            }
            *map.entry(ret.clone()).or_insert(0) = cost;
            q.push(Reverse((cost,ret.clone())));
        }
    }
    let ans = *map.get(&(String::new(),String::new(),true,true)).unwrap_or(&-1);
    println!("{}",ans);
}

fn judge(head: String, tail: String) -> (String,String,bool,bool) {
    let h = head.clone().chars().collect::<Vec<char>>();
    let t = tail.clone().chars().collect::<Vec<char>>();
    for i in 0..min(h.len(),t.len()) {
        if h[i]!=t[t.len()-1-i] {
            return (String::new(),String::new(),false,false);
        }
    }
    let s = head.clone() + &tail;
    let c = s.chars().collect::<Vec<char>>();
    let n = c.len();
    let mut flag = true;
    for i in 0..n {
        if c[i]!=c[n-1-i] {
            flag = false;
        }
    }
    if flag {
        return (String::new(),String::new(),true,true);
    }
    if h.len() > t.len() {
        let mut tmp = String::new();
        for i in t.len()..h.len() {
            tmp += &h[i].to_string();
        }
        return (tmp,String::new(),flag,true);
    }
    else {
        let mut tmp = String::new();
        for i in h.len()..t.len() {
            tmp += &t[i-head.len()].to_string();
        }
        return (String::new(),tmp,flag,true);
    }
}

fn run() {
    solve();
}