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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

DBG = !true

def rem(x)
  return if $bad[x]
  puts "rem #{x}" if DBG
  $live.delete(x)
  $bad[x] = true
  for j in $toa[x] + $tob[x]
    if $s[x] == 'A'
      $toa[j].delete(x)
      if j != x && $toa[j].empty?
        rem(j)
      end
    else
      $tob[j].delete(x)
      if j != x && $tob[j].empty?
        rem(j)
      end
    end
  end
  puts "rem return" if DBG
end

n,m = gets.split.map{|z| z.to_i}
$s = gets.chomp!
$toa = Array.new(n).map{[]}
$tob = Array.new(n).map{[]}
puts "n #{n} m #{m} s #{$s}" if DBG
for i in 0...m
  x,y = gets.split.map{|z| z.to_i - 1}
  puts "x #{x} y #{y}" if DBG
  if $s[x] == 'A'
    $toa[y] << x
  else
    $tob[y] << x
  end
  if y != x
    if $s[y] == 'A'
      $toa[x] << y
    else
      $tob[x] << y
    end
  end
  puts "$toa #{$toa} $tob #{$tob}" if DBG
end
$live = []
$bad = Array.new(n, false)
for i in 0...n
    $live << i
end
puts "setup done liv #{$live} bad #{$bad}" if DBG

chg = true
while chg
  chg = false
  for i in $live
    next if $bad[i]
    if $toa[i].empty? || $tob[i].empty?
      chg = true
      rem(i)
      puts "i #{i} toa #{$toa} tob #{$tob} " if DBG
      puts "   bad #{$bad} liv #{$live}" if DBG
    end
  end
end

print ($live.empty? ? 'No' : 'Yes')