Hand of Straights

hand[i] is the number on card i. Return True if the cards can be split into groups of exactly group_size cards where each group holds consecutive numbers (4, 5, 6 is a group of size 3).

For hand = [1, 2, 3, 6, 2, 3, 4, 7, 8] and group_size = 3 the answer is True ([1, 2, 3], [2, 3, 4], [6, 7, 8]).

Examples

Example 1

Input:

is_n_straight_hand([1, 2, 3, 6, 2, 3, 4, 7, 8], 3)

Output:

True

Example 2

Input:

is_n_straight_hand([1, 2, 3, 4, 5], 4)

Output:

False

Constraints

• 0 <= len(hand) <= 100000
• 1 <= group_size <= 100000
• 0 <= hand[i] <= 10**9