Multi-key Sorting

Input file:            keys.in                                                                                   100 points

Output file:         keys.out                                                                      Time limit: 6 sec

Source Code:    keys.pas/.c/.cpp                                           Memory limit:10 MB

Consider a table with rows and columns. The columns are numbered from 1 to C. For simplicity's sake, the items in the table are strings consisting of lower case letters.

Col. 1	Col. 2	Col. 3	Col. 1	Col. 2	Col. 3	Col. 1	Col. 2	Col. 3
apple	red	sweet	banana	brown	rotten	apple	green	sour
apple	green	sour	apple	green	sour	apple	red	sweet
pear	green	sweet	pear	green	sweet	banana	brown	rotten
banana	yellow	sweet	apple	red	sweet	banana	yellow	sweet
banana	brown	rotten	banana	yellow	sweet	pear	green	sweet

Table 1                                 Table 2                                     Table 3

You are given the operation Sort(k) on such tables: Sort(k) sorts the rows of a table in the order of the values in column k (while the order of the columns does not change). The sort is stable, that is, rows that have equal values in column k, remain in their original order. For example, applying Sort(2) to Table 1 yields Table 2.

We are interested in sequences of such sort operations. These operations are successively applied to the same table. For example, applying the sequence Sort(2); Sort(1) to Table 1 yields Table 3.

Two sequences of sort operations are called equivalent if, for any table, they have the same effect. For example, Sort(2); Sort(2); Sort(1) is equivalent to Sort(2); Sort(1). However, it is not equivalent to Sort(1); Sort(2), because the effect on Table 1 is different.

Task

Given a sequence of sort operations, determine a shortest equivalent sequence.

Input

The first line of the text file keys.in contains two integers, C and N. C (1 ≤ C ≤
 1 000 000) is the number of columns and N (1 ≤ N ≤ 3 000 000) is the number of sort operations. The second line contains N integers, k_i (1 ≤ k_i ≤ C). It defines the sequence of sort operations Sort(k₁); ...; Sort(k_N).

Output

The first line of the text file keys.out contains one integer, M, the length of the shortest sequence of sort operations equivalent to the input sequence (Subtask A). The second line contains exactly M integers, representing a shortest sequence (Subtask B). You can omit the second line if you solve only Subtask A.

Example

keys.in	keys.out
4 6 1 2 1 2 3 3	3 1 2 3