DFS

Time Limit: 5000/2000 MS (Java/Others)

Memory Limit: 65536/32768 K (Java/Others)

Description

A DFS(digital factorial sum) number is found by summing the factorial of every digit of a positive integer.

For example ,consider the positive integer 145 = 1!+4!+5!, so it's a DFS number.

Now you should find out all the DFS numbers in the range of int( [1, 2147483647] ).

There is no input for this problem. Output all the DFS numbers in increasing order. The first 2 lines of the output are shown below.

Input

no input

Output

Output all the DFS number in increasing order.

Sample Input

Sample Output

1 2 ......

Hint

lcy

Source


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