Problem:
Score : 900 points

Problem Statement

You are given an undirected graph consisting of N vertices and M edges.
The vertices are numbered 1 to N, and the edges are numbered 1 to M.
In addition, each vertex has a label, A or B. The label of Vertex i is s_i.
Edge i bidirectionally connects vertex a_i and b_i.

The phantom thief Nusook likes to choose some vertex as the startpoint and traverse an edge zero or more times.
Today, he will make a string after traveling as above, by placing the labels of the visited vertices in the order visited, beginning from the startpoint.

For example, in a graph where Vertex 1 has the label A and Vertex 2 has the label B, if Nusook travels along the path 1 \rightarrow 2 \rightarrow 1 \rightarrow 2 \rightarrow 2, the resulting string is ABABB.

Determine if Nusook can make all strings consisting of A and B.

Constraints

2 \leq N \leq 2 \times 10^{5}

1 \leq M \leq 2 \times 10^{5}

|s| = N

s_i is A or B.

1 \leq a_i, b_i \leq N

The given graph may NOT be simple or connected.

Input

Input is given from Standard Input in the following format:

N M
s
a_1 b_1
:
a_{M} b_{M}

Output

If Nusook can make all strings consisting of A and B, print Yes; otherwise, print No.

Sample Input 1

2 3
AB
1 1
1 2
2 2

Sample Output 1

Yes

Since Nusook can visit Vertex 1 and Vertex 2 in any way he likes, he can make all strings consisting of A and B.

Sample Input 2

4 3
ABAB
1 2
2 3
3 1

Sample Output 2

No

For example, Nusook cannot make BB.

The given graph may not be connected.

Sample Input 3

13 23
ABAAAABBBBAAB
7 1
10 6
1 11
2 10
2 8
2 11
11 12
8 3
7 12
11 2
13 13
11 9
4 1
9 7
9 6
8 13
8 6
4 10
8 7
4 3
2 1
8 12
6 9

Sample Output 3

Yes

Sample Input 4

13 17
BBABBBAABABBA
7 1
7 9
11 12
3 9
11 9
2 1
11 5
12 11
10 8
1 11
1 8
7 7
9 10
8 8
8 12
6 2
13 11

Sample Output 4

No

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

#[allow(unused_imports)]
use std::cmp::{min,max};
#[allow(unused_imports)]
use std::collections::{BTreeMap,BTreeSet};
#[allow(unused_imports)]
use std::ops::*;
#[allow(unused_imports)]
use std::collections::BinaryHeap;

#[allow(unused_macros)]
macro_rules! tf {
    ($c:expr, $t:expr, $f:expr) => {{
        if $c { $t } else { $f }
    }};
}
struct DisjointSet {
    ps: Vec<Option<usize>>,
    ns: Vec<i64>,
}

impl DisjointSet {
    fn new(n: usize) -> DisjointSet {
        DisjointSet { ps: vec![None; n], ns: vec![1; n] }
    }

    fn unite(&mut self, x: usize, y: usize) {
        let nx = self.find(x);
        let ny = self.find(y);
        if nx == ny {
            return;
        }
        let (a,b) = if self.ns[nx] < self.ns[ny] { (nx,ny) } else { (ny,nx) };
        self.ps[a] = Some(b);
        self.ns[b] += self.ns[a];
    }

    fn find(&mut self, x: usize) -> usize {
        match self.ps[x] {
            Some(y) => {
                let res = self.find(y);
                self.ps[x] = Some(res);
                res
            },
            None => {
                x
            },
        }
    }

    fn same(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }
}

fn main() {
    let (n,m) = {
        let xs = read_vec_i64();
        (xs[0] as usize, xs[1] as usize)
    };
    let ss: Vec<char> = read_line().chars().collect();
    let edges = {
        let mut edges = BTreeSet::new();
        for _ in 0..m {
            let xs = read_vec_i64();
            let s = (xs[0] - 1) as usize;
            let t = (xs[1] - 1) as usize;
            edges.insert((min(s,t), max(s,t)));
        }
        let mut res = vec![];
        for &(s,t) in &edges {
            res.push((s,t));
        }
        res
    };
    //eprintln!("{}", edges.len());
    let mut valid = vec![true; n];
    let mut code = vec![0; n];
    for _ in 0..10 {
        for &(s,t) in &edges {
            if !valid[s] || !valid[t] {
                continue;
            }
            if ss[s] == 'A' && ss[t] == 'A' {
                code[s] |= 0b0001;
                code[t] |= 0b0001;
            }
            if ss[s] == 'A' && ss[t] == 'B' {
                code[s] |= 0b0010;
                code[t] |= 0b0001;
            }
            if ss[s] == 'B' && ss[t] == 'A' {
                code[s] |= 0b0001;
                code[t] |= 0b0010;
            }
            if ss[s] == 'B' && ss[t] == 'B' {
                code[s] |= 0b0010;
                code[t] |= 0b0010;
            }
        }
        let mut d_set = DisjointSet::new(n);
        valid = vec![false; n];
        code = vec![0; n];
        for &(s,t) in &edges {
            if code[s] == 0b0011 && code[t] == 0b0011 {
                valid[s] = true;
                valid[t] = true;
            }
        }
    }
    let mut d_set = DisjointSet::new(n);
    for &(s,t) in &edges {
        if code[s] == 0b0011 && code[t] == 0b0011 {
            if d_set.same(s, t) {
                println!("Yes");
                return;
            }
            else {
                d_set.unite(s, t);
            }
        }
    }
    println!("No");
}

#[allow(dead_code)]
fn read_line() -> String {
    let mut ret = String::new();
    std::io::stdin().read_line(&mut ret).ok();
    ret.pop();
    //ret.pop();
    return ret;
}

#[allow(dead_code)]
fn read_i64() -> i64 {
    let ss = read_line();
    return ss.parse::<i64>().unwrap();
}

#[allow(dead_code)]
fn read_vec_i64() -> Vec<i64> {
    let mut res = vec![];
    let ss = read_line();
    for ts in ss.split_whitespace() {
        let x = ts.parse::<i64>().unwrap();
        res.push(x);
    }
    return res;
}

use std::fmt::Display;
#[allow(dead_code)]
fn write_vec<T: Display>(xs: &Vec<T>) {
    if xs.len() == 0 {
        println!("");
        return;
    }
    print!("{}", xs[0]);
    for i in 1..xs.len() {
        print!(" {}", xs[i]);
    }
    println!("");
}