Problem:
Score : 1500 points

Problem Statement

You are given a tree with N vertices numbered 1, 2, ..., N. The i-th edge connects Vertex a_i and Vertex b_i.
You are also given a string S of length N consisting of 0 and 1. The i-th character of S represents the number of pieces placed on Vertex i.

Snuke will perform the following operation some number of times:

Choose two pieces the distance between which is at least 2, and bring these pieces closer to each other by 1. More formally, choose two vertices u and v, each with one or more pieces, and consider the shortest path between them. Here the path must contain at least two edges. Then, move one piece from u to its adjacent vertex on the path, and move one piece from v to its adjacent vertex on the path.

By repeating this operation, Snuke wants to have all the pieces on the same vertex. Is this possible?
If the answer is yes, also find the minimum number of operations required to achieve it.

Constraints

2 \leq N \leq 2000

|S| = N

S consists of 0 and 1, and contains at least one 1.

1 \leq a_i, b_i \leq N(a_i \neq b_i)

The edges (a_1, b_1), (a_2, b_2), ..., (a_{N - 1}, b_{N - 1}) forms a tree.

Input

Input is given from Standard Input in the following format:

N
S
a_1 b_1
a_2 b_2
:
a_{N - 1} b_{N - 1}

Output

If it is impossible to have all the pieces on the same vertex, print -1. If it is possible, print the minimum number of operations required.

Sample Input 1

7
0010101
1 2
2 3
1 4
4 5
1 6
6 7

Sample Output 1

3

We can gather all the pieces in three operations as follows:

Choose the pieces on Vertex 3 and 5.

Choose the pieces on Vertex 2 and 7.

Choose the pieces on Vertex 4 and 6.

Sample Input 2

7
0010110
1 2
2 3
1 4
4 5
1 6
6 7

Sample Output 2

-1

Sample Input 3

2
01
1 2

Sample Output 3

0

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

#![allow(non_snake_case, unused_imports)]
//////////////////////////////// LIBRARY START ////////////////////////////////
#[macro_use]
pub mod contest {
    #[macro_use]
    pub mod prelude {
        pub use self::myvec::*;
        #[macro_use]
        pub mod primitive {
            pub trait ToUsize: Sized {
                fn to_usize(self) -> usize;
            }

            impl ToUsize for i32 {
                #[inline]
                fn to_usize(self) -> usize {
                    self as usize
                }
            }

            impl ToUsize for i64 {
                #[inline]
                fn to_usize(self) -> usize {
                    self as usize
                }
            }

            impl ToUsize for usize {
                #[inline]
                fn to_usize(self) -> usize {
                    self
                }
            }
        }
        #[macro_use]
        pub mod myvec {
            use std::fmt;
            use std::iter::FromIterator;
            use std::ops::*;

            pub use super::primitive::ToUsize;

            /// `Vec` indexable with `i32`, `i64` or `usize`.
            #[derive(Clone, Debug, PartialEq, PartialOrd)]
            pub struct MyVec<T>(pub Vec<T>);

            /// Creates `MyVec`
            #[macro_export]
            macro_rules! v {
    ( $( $x:expr ),* ) => {
        MyVec(vec![ $( $x, )* ])
    };
    ( $x:expr ; $n:expr ) => {
        {
            MyVec(vec![$x; $n as usize])
        }
    };
}

            impl<T: fmt::Display> fmt::Display for MyVec<T> {
                fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
                    let n = self.len();
                    for i in 0..n {
                        let r = if i < n - 1 {
                            writeln!(f, "{}", self.0[i])
                        } else {
                            write!(f, "{}", self.0[i])
                        };
                        if r.is_err() {
                            return r;
                        }
                    }
                    Ok(())
                }
            }

            impl<T> Deref for MyVec<T> {
                type Target = Vec<T>;

                #[inline]
                fn deref(&self) -> &Vec<T> {
                    &self.0
                }
            }

            impl<T> DerefMut for MyVec<T> {
                #[inline]
                fn deref_mut(&mut self) -> &mut Vec<T> {
                    &mut self.0
                }
            }

            impl<T> FromIterator<T> for MyVec<T> {
                #[inline]
                fn from_iter<I: IntoIterator<Item = T>>(iter: I) -> Self {
                    MyVec(Vec::from_iter(iter))
                }
            }

            impl<T, I: ToUsize> Index<I> for MyVec<T> {
                type Output = T;

                #[inline]
                fn index(&self, i: I) -> &T {
                    &self.0[i.to_usize()]
                }
            }

            impl<T, I: ToUsize> IndexMut<I> for MyVec<T> {
                #[inline]
                fn index_mut(&mut self, i: I) -> &mut T {
                    &mut self.0[i.to_usize()]
                }
            }

            #[test]
            fn test_myvec() {
                let mut x = v![3, 2, 1];
                x.sort();
                assert_eq!(vec![1, 2, 3], *x);
                let i = 1i32;
                assert_eq!(2, x[i]);
                x[i] = 3;
                assert_eq!(3, x[i]);
                let u = 1usize;
                assert_eq!(3, x[u]);
                x[u] = 2;
                assert_eq!(2, x[u]);
                assert_eq!(2, x[1]);

                assert_eq!("MyVec([1, 2, 3])", format!("{:?}", x));
                assert_eq!(v![1, 2, 3], x);

                assert_eq!("1\n2\n3", format!("{}", x));

                let mut y = v![v![1, 2]; 3];
                y[0][0] = 2;
                assert_eq!(vec![2, 2], *y[0]);
                assert_eq!(vec![1, 2], *y[1]);
            }
        }
    }
    #[macro_use]
    pub mod io {
        /// Scanner
        ///
        /// # Example
        /// ```
        /// use contest::io::Scanner;
        /// let mut sc = Scanner::new("1 2 \n\n \r\t \n 3".as_bytes());
        /// assert_eq!("1".to_string(), sc.next::<String>());
        /// let v = sc.nexts(2);
        /// assert_eq!(2i32, v[0]);
        /// assert_eq!(3i32, v[1]);
        ///
        /// // To create a scanner from stdin:
        /// Scanner::new(std::io::stdin());
        /// ```
        use std;
        use std::io;
        use std::io::BufRead;

        use super::prelude::MyVec;

        pub struct Scanner<R: io::Read> {
            br: io::BufReader<R>,
            // Read tokens are stored in reversed order per line.
            buf: Vec<String>,
        }

        pub fn new<R: io::Read>(r: R) -> Scanner<R> {
            Scanner::new(r)
        }

        impl<R: io::Read> Scanner<R> {
            #[inline]
            pub fn new(r: R) -> Scanner<R> {
                Scanner {
                    br: io::BufReader::new(r),
                    buf: vec![],
                }
            }
            #[inline]
            pub fn next<T>(&mut self) -> T
            where
                T: std::str::FromStr,
                T::Err: std::fmt::Debug,
            {
                self.next_string()
                    .map(|s| s.parse::<T>().expect("Parse failed: "))
                    .expect("Unexpected EOF")
            }
            #[inline]
            pub fn nexts<T>(&mut self, n: i32) -> MyVec<T>
            where
                T: std::str::FromStr,
                T::Err: std::fmt::Debug,
            {
                let mut res = v![];
                for _ in 0..n {
                    res.push(self.next());
                }
                res
            }
            fn next_string(&mut self) -> Option<String> {
                self.buf.pop().or_else(|| match self.update() {
                    true => self.next_string(),
                    false => None,
                })
            }
            #[inline]
            fn update(&mut self) -> bool {
                let mut s = String::new();
                let res = self.br.read_line(&mut s);
                match res.expect("I/O error.") {
                    0 => false,
                    _ => {
                        self.buf = s.split_whitespace().map(|x| x.to_string()).rev().collect();
                        true
                    }
                }
            }
        }

        #[test]
        fn test_next() {
            let mut sc = new("hoge".as_bytes());
            let s: String = sc.next();
            assert_eq!("hoge", s);
        }
    }
}
//////////////////////////////// LIBRARY END ////////////////////////////////

use contest::io::Scanner;
use contest::prelude::MyVec;

const INF: i32 = 1_000_000_000;
fn main() {
    let mut sc = Scanner::new(std::io::stdin());

    let n = sc.next::<i32>();
    let s = sc.next::<String>();

    let mut graph = v![v![]; n];
    for i in 0..(n - 1) {
        let a = sc.next::<i32>() - 1;
        let b = sc.next::<i32>() - 1;
        graph[a].push(b);
        graph[b].push(a);
    }
    let mut have = v![];
    for c in s.chars() {
        have.push(c == '1');
    }

    let mut res = INF;
    for i in 0..n {
        let (min, max, _) = dfs(&graph, &have, i, -1);
        if min == 0 {
            if res > max / 2 {
                res = max / 2;
            }
        }
    }

    println!("{}", if res == INF { -1 } else { res });
}

fn dfs(graph: &MyVec<MyVec<i32>>, have: &MyVec<bool>, root: i32, parent: i32) -> (i32, i32, i32) {
    // min, max, num
    let mut tot = 0;
    let mut res_min = 0;
    let mut res_max = 0;
    for j in &*graph[root] {
        if *j == parent {
            continue;
        }
        let tup = dfs(graph, have, *j, root);
        let mut min = tup.0;
        let mut max = tup.1;
        let num = tup.2;
        tot += num;
        min += num;
        max += num;

        if max < res_min {
            res_min = res_min - max;
        } else if res_max < min {
            res_min = min - res_max;
        } else {
            if ((res_min + min) & 1) == 0 {
                res_min = 0;
            } else {
                res_min = 1;
            }
        }
        res_max += max;
    }
    if have[root] {
        tot += 1;
    }
    (res_min, res_max, tot)
}