Insert Algorithm:

The Robinson Schensted Knuth corresponding Standard Young Tableaux may be computed by the Insert Algorithm. Here we consider the tables which encode a permutation π(q).

Begin with q = 1 and the empty tables P and Q.
(a) Set x = π(q), and insert x into table P as prescribed in (b), starting on the first row.
(b) Insert x into current row as follows:

• If x is larger than all entries in the row:
  1. Append the value x at the end of the current row.
  2. Append the value q to the end of the corresponding row in table Q.
  3. Increase q, then repeat (a)
• If not, there is a row entry β > x that is minimal.
  1. Switch the values of β and x.
  2. Insert the new x into the next row as prescribed in (b). ( insert new x into new current row)

Enter a valid permutation in word form to compute a new pair of tables.