Problem:
Score : 400 points

Problem Statement

There are N squares arranged in a row, numbered 1, 2, ..., N from left to right.
You are given a string S of length N consisting of . and #. If the i-th character of S is #, Square i contains a rock; if the i-th character of S is ., Square i is empty.

In the beginning, Snuke stands on Square A, and Fnuke stands on Square B.

You can repeat the following operation any number of times:

Choose Snuke or Fnuke, and make him jump one or two squares to the right. The destination must be one of the squares, and it must not contain a rock or the other person.

You want to repeat this operation so that Snuke will stand on Square C and Fnuke will stand on Square D.

Determine whether this is possible.

Constraints

4 \leq N \leq 200\ 000

S is a string of length N consisting of . and #.

1 \leq A, B, C, D \leq N

Square A, B, C and D do not contain a rock.

A, B, C and D are all different.

A < B

A < C

B < D

Input

Input is given from Standard Input in the following format:

N A B C D
S

Output

Print Yes if the objective is achievable, and No if it is not.

Sample Input 1

7 1 3 6 7
.#..#..

Sample Output 1

Yes

The objective is achievable by, for example, moving the two persons as follows. (A and B represent Snuke and Fnuke, respectively.)

A#B.#..

A#.B#..

.#AB#..

.#A.#B.

.#.A#B.

.#.A#.B

.#..#AB

Sample Input 2

7 1 3 7 6
.#..#..

Sample Output 2

No

Sample Input 3

15 1 3 15 13
...#.#...#.#...

Sample Output 3

Yes

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

N, A, B, C, D = gets.chomp.split(" ").map(&:to_i)
s = []
s = gets.chomp.split("")

# すぬけ君の初期位置と可能性
$sunuke = {:point => A - 1, :able => nil, :goal => C - 1}
# ふぬけ君の初期位置と可能性
$funuke = {:point => B - 1, :able => nil, :goal => D - 1}

# ケンケンを表す再帰関数
# もう片方の相手にぶつかってこれ以上進めなくなった時にはバトンを渡して、
# もしくは前後が空いている追い越しポイントにたどり着いた時にはバトンを渡さず
# もう片方の相手に交代する。
# バトンは無限ループを防ぐためのパラメータ
def kenken(walker, batton, s)
  # p walker
  if walker == "sunuke" then
    # もし目的地にたどり着いたら
    if $sunuke[:point] == $sunuke[:goal] then
      $sunuke[:able] = true

    # elsif $sunuke[:point] - 1 == $funuke[:point] && !batton then
    #   kenken("funuke", false, s)

    # もしふぬけ君にぶつかって進めなくなったら
    # ふぬけ君にバトンを渡して交代
    # ただし、ふぬけ君がゴールにたどり着いていない限り
    elsif ($sunuke[:point] + 1 == $funuke[:point] && s[$sunuke[:point] + 2] == "#" \
      || $sunuke[:point] + 2 == $funuke[:point] && s[$sunuke[:point] + 1] == "#") \
      && $funuke[:point] != $funuke[:goal] then
      kenken("funuke", false, s)

    # もし追い越しポイントにたどり着いたら
    # ふぬけ君にバトンを渡さず交代
    elsif s[$sunuke[:point] - 1] == "." && s[$sunuke[:point] + 1] == "." && \
          $sunuke[:point] - 1 > 0 && batton then
      kenken("funuke", false, s)

    # 一つ前に進めるのなら
    elsif s[$sunuke[:point] + 1] == "." && $sunuke[:point] + 1 != $funuke[:point] then
      $sunuke[:point] += 1
      # p "sunuke"
      # p $sunuke[:point] + 1
      kenken("sunuke", true, s)

    # 二つ前に進めるのなら
    elsif s[$sunuke[:point] + 2] == "." && $sunuke[:point] + 2 != $funuke[:point] then
      $sunuke[:point] += 2
      # p "sunuke"
      # p $sunuke[:point] + 1
      kenken("sunuke", true, s)

    else
      $sunuke[:able] = false
    end
  elsif walker == "funuke" then
    # もし目的地にたどり着いたら
    if $funuke[:point] == $funuke[:goal] then
      $funuke[:able] = true

    # elsif $funuke[:point] - 1 == $sunuke[:point] && !batton then
    #   kenken("sunuke", false, s)

    # もしすぬけ君にぶつかって進めなくなったら
    # すぬけ君にバトンを渡して交代
    # ただし、すぬけ君がゴールにたどり着いていない限り
  elsif ($funuke[:point] + 1 == $sunuke[:point] && s[$funuke[:point] + 2] == "#" \
      || $funuke[:point] + 2 == $sunuke[:point] && s[$funuke[:point] + 1] == "#") \
      && $sunuke[:point] != $sunuke[:goal] then
      kenken("sunuke", false, s)

    # もし追い越しポイントにたどり着いたら
    # すぬけ君にバトンを渡さず交代
    elsif s[$funuke[:point] - 1] == "." && s[$funuke[:point] + 1] == "." && \
          $funuke[:point] - 1 > 0 && batton then
      kenken("sunuke", false, s)

    # 一つ前に進めるのなら
    elsif s[$funuke[:point] + 1] == "." && $funuke[:point] + 1 != $sunuke[:point] then
      $funuke[:point] += 1
      # p "funuke"
      # p $funuke[:point] + 1
      kenken("funuke", true, s)

    # 二つ前に進めるのなら
    elsif s[$funuke[:point] + 2] == "." && $funuke[:point] + 2 != $sunuke[:point] then
      $funuke[:point] += 2
      # p "funuke"
      # p $funuke[:point] + 1
      kenken("funuke", true, s)

    else
      $funuke[:able] = false
    end
  end
  if $sunuke[:able] && $funuke[:able] then
    true
  elsif $sunuke[:able] == nil then
    kenken("sunuke", false, s)
  elsif $funuke[:able] == nil then
    kenken("funuke", false, s)
  end
end

# puts sunuke[:point]
# puts funuke[:able]

kenken("sunuke", false, s)

if $sunuke[:able] && $funuke[:able] then
  puts "Yes"
else
  puts "No"
end