Flip a fair coin n times, where n is even. Return (expected_heads, std_dev, p_exactly_expected):

• the expected number of heads
• the standard deviation of the count
• the probability of landing on exactly that expected number

The third value surprises people: the most likely single outcome still has a small probability, and it shrinks as n grows even though the distribution tightens around it.

Input

100

Output

(50.0, 5.0, 0.07958923738717877)