// output of ./demo/comb/setpart-p-rgs-lex-demo.cc:
// Description:
//% Set partitions into p parts as restricted growth strings (RGS).

arg 1: 5 == n  [Partition set of n elements]  default=5
arg 2: 3 == p  [Partitions into p parts (2<=p<=n)]  default=3
  1:  {1, 2, 3}, {4}, {5}    s[ 0 0 0 1 2 ]    m[ 1 1 1 2 3 ]
  2:  {1, 2, 4}, {3}, {5}    s[ 0 0 1 0 2 ]    m[ 1 1 2 2 3 ]
  3:  {1, 2}, {3, 4}, {5}    s[ 0 0 1 1 2 ]    m[ 1 1 2 2 3 ]
  4:  {1, 2, 5}, {3}, {4}    s[ 0 0 1 2 0 ]    m[ 1 1 2 3 3 ]
  5:  {1, 2}, {3, 5}, {4}    s[ 0 0 1 2 1 ]    m[ 1 1 2 3 3 ]
  6:  {1, 2}, {3}, {4, 5}    s[ 0 0 1 2 2 ]    m[ 1 1 2 3 3 ]
  7:  {1, 3, 4}, {2}, {5}    s[ 0 1 0 0 2 ]    m[ 1 2 2 2 3 ]
  8:  {1, 3}, {2, 4}, {5}    s[ 0 1 0 1 2 ]    m[ 1 2 2 2 3 ]
  9:  {1, 3, 5}, {2}, {4}    s[ 0 1 0 2 0 ]    m[ 1 2 2 3 3 ]
 10:  {1, 3}, {2, 5}, {4}    s[ 0 1 0 2 1 ]    m[ 1 2 2 3 3 ]
 11:  {1, 3}, {2}, {4, 5}    s[ 0 1 0 2 2 ]    m[ 1 2 2 3 3 ]
 12:  {1, 4}, {2, 3}, {5}    s[ 0 1 1 0 2 ]    m[ 1 2 2 2 3 ]
 13:  {1}, {2, 3, 4}, {5}    s[ 0 1 1 1 2 ]    m[ 1 2 2 2 3 ]
 14:  {1, 5}, {2, 3}, {4}    s[ 0 1 1 2 0 ]    m[ 1 2 2 3 3 ]
 15:  {1}, {2, 3, 5}, {4}    s[ 0 1 1 2 1 ]    m[ 1 2 2 3 3 ]
 16:  {1}, {2, 3}, {4, 5}    s[ 0 1 1 2 2 ]    m[ 1 2 2 3 3 ]
 17:  {1, 4, 5}, {2}, {3}    s[ 0 1 2 0 0 ]    m[ 1 2 3 3 3 ]
 18:  {1, 4}, {2, 5}, {3}    s[ 0 1 2 0 1 ]    m[ 1 2 3 3 3 ]
 19:  {1, 4}, {2}, {3, 5}    s[ 0 1 2 0 2 ]    m[ 1 2 3 3 3 ]
 20:  {1, 5}, {2, 4}, {3}    s[ 0 1 2 1 0 ]    m[ 1 2 3 3 3 ]
 21:  {1}, {2, 4, 5}, {3}    s[ 0 1 2 1 1 ]    m[ 1 2 3 3 3 ]
 22:  {1}, {2, 4}, {3, 5}    s[ 0 1 2 1 2 ]    m[ 1 2 3 3 3 ]
 23:  {1, 5}, {2}, {3, 4}    s[ 0 1 2 2 0 ]    m[ 1 2 3 3 3 ]
 24:  {1}, {2, 5}, {3, 4}    s[ 0 1 2 2 1 ]    m[ 1 2 3 3 3 ]
 25:  {1}, {2}, {3, 4, 5}    s[ 0 1 2 2 2 ]    m[ 1 2 3 3 3 ]
 ct = 25