Generate strong primes In number theory, a strong prime is a prime number that is greater than the arithmetic mean of the nearest prime above and below (in other words, it's closer to the following than to the preceding prime).


Given an input integer, n, where n &gt;= 0, your task is to generate the first n strong primes. For example, the sixth, seventh, and eighth primes are 13, 17, and 19, respectively:

(13 + 19) / 2 &lt; 17


Therefore, 17 is a strong prime.

Input


an integer


Output


if n is 0


program: output nothing
function: return an empty array

if n is greater than 0


program: output the first n strong primes, each on its own line
function: return an array containing the first n strong primes



Test cases

0
[]

4
[11, 17, 29, 37]

7
[11, 17, 29, 37, 41, 59, 67]

47
[11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439, 457, 461, 479, 487, 499, 521, 541, 557, 569, 587, 599]


See also: Strong primes on OEIS
Husk, 12 11 bytes

↑§foẊ&lt;Ẋ-tİp


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-1 byte thanks to H.PWiz.

Explanation

↑§foẊ&lt;Ẋ-tİp  Input is n.
         İp  The infinite list of primes.
      Ẋ-     Take pairwise differences,
   oẊ&lt;       then pairwise comparisons.
        t    Frop the first element from İp
 §f          and filter the rest using the result of oẊ&lt;Ẋ-.
↑            Take first n elements of this list.