Statement

Please pay attention to the special time limit

Wanna play some game?

Let's define a token to be a 6-digit integer string. Leading zeros are allowed. For example, "123456" "000000" are tokens while "A12345" "1" are not.

Let's define the Longest Common Prefix of two strings S and T to be the the maximum integer K so that $S[1:K]=T[1:K]$. For example, the LCP of "123456" and "123654" is 3, the one of "123456" and "654321" is 0.

There's a secret token $S$. It's determined independently from your input and randomly but it is generated after your program finishes.

You are also given an array $L$ of length 6. You are also given a function $f$ which could be max or sum.

You can output any numbers of tokens $T$, let's say $N$.

Your score will be determined as $f(L_{LCP(T_1,S)},...,L_{LCP(T_N,S)})/N/max(L_1,...,L_6,1)$

Task

Write a program that:

• Read L1 to L6 from STDIN and f
• Output the number of tokens then some tokens one in a line.
• Halt.

Input

Six integers L1 to L6 then f. $0\leq L_i\leq 10^5$

f can only be max or sum.

Output

On the first line, print N, the number of tokens($1\leq N\leq 10^5$)

then on the i-th line, print the i-th token.

Example

[In]
1 2 3 4 5 6 sum
[Output]
3
123456
654321
114114

Explain:

If the secret token is "114514". the score is $\frac{1+0+3}{3}=\frac{4}{3}$