Problem:
Score : 600 points

Problem Statement

A bracket sequence is a string that is one of the following:

An empty string;

The concatenation of (, A, and ) in this order, for some bracket sequence A ;

The concatenation of A and B in this order, for some non-empty bracket sequences A and B /

Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?

Constraints

1 \leq N \leq 10^6

The total length of the strings S_i is at most 10^6.

S_i is a non-empty string consisting of ( and ).

Input

Input is given from Standard Input in the following format:

N
S_1
:
S_N

Output

If a bracket sequence can be formed by concatenating all the N strings in some order, print Yes; otherwise, print No.

Sample Input 1

2
)
(()

Sample Output 1

Yes

Concatenating (() and ) in this order forms a bracket sequence.

Sample Input 2

2
)(
()

Sample Output 2

No

Sample Input 3

4
((()))
((((((
))))))
()()()

Sample Output 3

Yes

Sample Input 4

3
(((
)
)

Sample Output 4

No

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

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
#![macro_use]

use std::cmp::*;
use std::collections::*;
use std::io::*;
use std::mem::*;
use std::num::*;
use std::slice::*;

fn check(s: &Vec<(isize, isize)>) -> bool {
    let mut h = 0;
    for p in s.iter() {
        let b = h + p.0;
        if b < 0 {
            return false;
        }
        h += p.1;
    }
    true
}

fn main() {
    let mut io = IO::new(stdin(), stdout(), stderr());
    // ===================================== //
    let n: usize = io.read();
    let mut ls: Vec<(isize, isize)> = Vec::new();
    let mut rs: Vec<(isize, isize)> = Vec::new();
    let mut total = 0;
    for i in 0..n {
        let mut s = io.chars();
        let mut h: isize = 0;
        let mut b: isize = 0;
        for &c in s.iter() {
            if c == '(' {
                h += 1;
            } else {
                h -= 1;
            }
            b = min(b, h);
        }
        if h > 0 {
            ls.push((b, h));
        } else {
            rs.push((b - h, -h));
        }
        total += h;
    }
    ls.sort_by(|a, b| b.cmp(a));
    rs.sort_by(|a, b| b.cmp(a));
    if check(&ls) && check(&rs) && total == 0 {
        io.writeln("Yes");
    } else {
        io.writeln("No");
    }
}

// IO
struct IO<R: Read, W: Write, E: Write> {
    Read: R,
    Write: BufWriter<W>,
    Error: BufWriter<E>,
}
impl<R: Read, W: Write, E: Write> IO<R, W, E> {
    fn new(r: R, w: W, e: E) -> IO<R, W, E> {
        IO {
            Read: r,
            Write: BufWriter::new(w),
            Error: BufWriter::new(e),
        }
    }
    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
    {
        let next: String = self
            .Read
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect();
        next.parse().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
    fn readn<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read::<T>()).collect::<Vec<_>>()
    }
    fn readmat<T: std::str::FromStr>(&mut self, n: usize, m: usize) -> Vec<Vec<T>> {
        (0..n).map(|_| self.readn(m)).collect()
    }
    fn write<S: ToString>(&mut self, val: S) {
        self.Write.write(val.to_string().as_bytes());
    }
    fn writeln<S: ToString>(&mut self, val: S) {
        self.Write.write(val.to_string().as_bytes());
        self.Write.write(b"\n");
    }
    fn debug<S: std::fmt::Debug>(&mut self, val: S) {
        writeln!(self.Error, "(debug) {:?}", &val);
    }
}