Problem:
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Dice III

Write a program which reads the two dices constructed in the same way as Dice I, and determines whether these two dices are identical. You can roll a dice in the same way as Dice I, and if all integers observed from the six directions are the same as that of another dice, these dices can be considered as identical.

Input

In the first line, six integers assigned to faces of a dice are given in ascending order of their corresponding labels.

In the second line, six integers assigned to faces of another dice are given in ascending order of their corresponding labels.

Output

Print "Yes" if two dices are identical, otherwise "No" in a line.

Constraints

$0 \leq $ the integer assigned to a face $ \leq 100$

Sample Input 1

1 2 3 4 5 6
6 2 4 3 5 1

Sample Output 1

Yes

Sample Input 2

1 2 3 4 5 6
6 5 4 3 2 1

Sample Output 2

No

Solution in Ruby (judge verdict: Wrong Answer)

if (_dice_a = gets.split.map(&:to_i)) == (_dice_b = gets.split.map(&:to_i))
  puts "Yes"
  exit
elsif _dice_a.uniq.size == 1
  puts "Yes"
  exit
end

def vertical_roll(new_dice, upper_value)
  count = 0
  while new_dice[0] != upper_value && count < 4
    new_dice[0], new_dice[1], new_dice[4], new_dice[5] = new_dice[1], new_dice[5], new_dice[0], new_dice[4]
  end
  new_dice
end

def horizontal_roll(new_dice, front_value)
  count = 0
  while new_dice[1] != front_value && count < 4
    new_dice[1], new_dice[2], new_dice[4], new_dice[3] = new_dice[2], new_dice[4], new_dice[3], new_dice[1]
    count += 1
  end
  new_dice
end

_dice_b_idx = _dice_b.index(_dice_a[0])

case _dice_b_idx
when 0, 1, 5, 4
  vertical_roll(_dice_b, _dice_a[0])
  horizontal_roll(_dice_b, _dice_a[1])
else
  horizontal_roll(_dice_b, _dice_a[0])
  vertical_roll(_dice_b, _dice_a[0])
  horizontal_roll(_dice_b, _dice_a[1])
end

puts _dice_a == _dice_b ? "Yes" : "No"