beecrowd | 1801 | [Univ]
# Playing with Numbers

**Timelimit: 3**

By Fidel I. Schaposnik Massolo, Universidad Nacional de La Plata Argentina

Prof. Cedrado-Cueta likes to play with numbers, and he is particularly fond of perfect squares. A natural number *n* is said to be a perfect square if there exists a natural number *m* such that *n* = *m*^{2}. For example, 9 and 36 are perfect squares because 9 = 3^{2} and 36 = 6^{2}, whereas 5 and 12 are not perfect squares.

The Prof. recently found a number *x*, and he would like to create a perfect square using it. In order to do so, he will reorder the digits of *x* to form some number *y*, and then calculate *n* = *x* + *y*. In how many ways is it possible for him to obtain a perfect square as the value of *n*? For example, if *x* = 29 the Prof. can take *y* = 92, so that *n* = 29 + 92 = 121 = 11^{2}.

Note that when reordering the digits of *x* the Prof. should use all its digits and obtain a correct expression for the number *y*, i.e. there can be no leading 0's in *y*. Also note that he may choose to keep the digits of *x* in the same order, effectively getting for *y* the same value as *x*.

The input consists of a single line containing one positive integer number *x* with at most 12 digits.

The output consists of a single line containing one integer number representing the number of ways in which the Prof. can obtain a perfect square as the value of *n*. Two ways are considered different if they differ in the value of *n* obtained.

Input Samples | Output Samples |

2 |
1 |

511 |
0 |

1234567890 |
67 |