output_description: Print the maximum number of times the operation can be applied.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
attempt: N = int(input())
  primeNum = [
      2,
      3,
      5,
      7,
      11,
      13,
      17,
      19,
      23,
      29,
      31,
      37,
      41,
      43,
      47,
      53,
      59,
      61,
      67,
      71,
      73,
      79,
      83,
      89,
      97,
      101,
      103,
      107,
      109,
      113,
      127,
      131,
      137,
      139,
      149,
      151,
      157,
      163,
      167,
      173,
      179,
      181,
      191,
      193,
      197,
      199,
      211,
      223,
      227,
      229,
      233,
      239,
      241,
      251,
      257,
      263,
      269,
      271,
      277,
      281,
      283,
      293,
      307,
      311,
      313,
      317,
      331,
      337,
      347,
      349,
      353,
      359,
      367,
      373,
      379,
      383,
      389,
      397,
      401,
      409,
      419,
      421,
      431,
      433,
      439,
      443,
      449,
      457,
      461,
      463,
      467,
      479,
      487,
      491,
      499,
      503,
      509,
      521,
      523,
      541,
      547,
      557,
      563,
      569,
      571,
      577,
      587,
      593,
      599,
      601,
      607,
      613,
      617,
      619,
      631,
      641,
      643,
      647,
      653,
      659,
      661,
      673,
      677,
      683,
      691,
      701,
      709,
      719,
      727,
      733,
      739,
      743,
      751,
      757,
      761,
      769,
      773,
      787,
      797,
      809,
      811,
      821,
      823,
      827,
      829,
      839,
      853,
      857,
      859,
      863,
      877,
      881,
      883,
      887,
      907,
      911,
      919,
      929,
      937,
      941,
      947,
      953,
      967,
      971,
      977,
      983,
      991,
      997,
      1009,
      1013,
      1019,
      1021,
      1031,
      1033,
      1039,
      1049,
      1051,
      1061,
      1063,
      1069,
      1087,
      1091,
      1093,
      1097,
      1103,
      1109,
      1117,
      1123,
      1129,
      1151,
      1153,
      1163,
      1171,
      1181,
      1187,
      1193,
      1201,
      1213,
      1217,
      1223,
      1229,
      1231,
      1237,
      1249,
      1259,
      1277,
      1279,
      1283,
      1289,
      1291,
      1297,
      1301,
      1303,
      1307,
      1319,
      1321,
      1327,
      1361,
      1367,
      1373,
      1381,
      1399,
      1409,
      1423,
      1427,
      1429,
      1433,
      1439,
      1447,
      1451,
      1453,
      1459,
      1471,
      1481,
      1483,
      1487,
      1489,
      1493,
      1499,
      1511,
      1523,
      1531,
      1543,
      1549,
      1553,
      1559,
      1567,
      1571,
      1579,
      1583,
      1597,
      1601,
      1607,
      1609,
      1613,
      1619,
      1621,
      1627,
      1637,
      1657,
      1663,
      1667,
      1669,
      1693,
      1697,
      1699,
      1709,
      1721,
      1723,
      1733,
      1741,
      1747,
      1753,
      1759,
      1777,
      1783,
      1787,
      1789,
      1801,
      1811,
      1823,
      1831,
      1847,
      1861,
      1867,
      1871,
      1873,
      1877,
      1879,
      1889,
      1901,
      1907,
      1913,
      1931,
      1933,
      1949,
      1951,
      1973,
      1979,
      1987,
      1993,
      1997,
      1999,
  ]
  
  pow = 1
  time = 0
  while True:
      for p in primeNum:
          z = p**pow
          if p <= N:
              if N % z == 0:
                  N = int(N / (z))
                  time += 1
                  print(N)
          else:
              break
      pow += 1
      if pow >= N:
          break
  
  print(time)
  
problem_description: Statement
  
  Given is a positive integer N. Consider repeatedly applying the operation
  below on N:
  
    * First, choose a positive integer z satisfying all of the conditions below:
      * z can be represented as z=p^e, where p is a prime number and e is a positive integer;
      * z divides N;
      * z is different from all integers chosen in previous operations.
    * Then, replace N with N/z.
  
  Find the maximum number of times the operation can be applied.
samples: [{"input": "24", "output": "3\n    \n\nWe can apply the operation three times by, for example, making the following\nchoices:\n\n  * Choose z=2 (=2^1). (Now we have N=12.)\n  * Choose z=3 (=3^1). (Now we have N=4.)\n  * Choose z=4 (=2^2). (Now we have N=1.)\n\n* * *"}, {"input": "1", "output": "0\n    \n\nWe cannot apply the operation at all.\n\n* * *"}, {"input": "64", "output": "3\n    \n\nWe can apply the operation three times by, for example, making the following\nchoices:\n\n  * Choose z=2 (=2^1). (Now we have N=32.)\n  * Choose z=4 (=2^2). (Now we have N=8.)\n  * Choose z=8 (=2^3). (Now we have N=1.)\n\n* * *"}, {"input": "1000000007", "output": "1\n    \n\nWe can apply the operation once by, for example, making the following choice:\n\n  * z=1000000007 (=1000000007^1). (Now we have N=1.)\n\n* * *"}, {"input": "997764507000", "output": "7"}]