Star Battles I
A Star Battle (of the $2$star variety), also known as “Two Not Touch” as published by The New York Times, is a solitary starplacement puzzle played on a $10\times 10$ grid. The grid is divided into exactly ten $4$connected regions, and the objective is to place exactly $20$ stars in the grid, each in its own cell, such that following conditions are satisfied:

Every row, column, and region of the grid contains exactly two stars.

No two stars are in adjacent cells, i.e. cells next to each other horizontally, vertically, or diagonally.
Below is an example of a Star Battle puzzle,^{1} where regions are delimited by bold lines. The unique solution to this puzzle is shown on the right.
Given a description of a Star Battle puzzle and a candidate solution, your task for this problem is to write a program that will determine whether or not the candidate is indeed a valid solution to the puzzle. The input to your program is guaranteed to be a valid Star Battle puzzle with a unique solution.
Input
The first $10$ lines of input contain a description of the Star Battle puzzle. Every line contains exactly $10$ digits, where the digit names the region to which its cell belongs. There will be exactly $10$ contiguous, $4$connected (i.e. left, right, top, bottom, but not diagonal) regions in the puzzle.
The next $10$ lines of input contain a description of the candidate solution. Every line contains exactly $10$ characters, each a ‘.’ to indicate an empty cell or a ‘*’ to indicate placement of a star.
Output
If the candidate solution is consistent with all the Star Battle rules for the provided puzzle, output the word “valid” on a single line. Otherwise, output “invalid”.
Sample Input 1  Sample Output 1 

0001111223 0001221223 0001222223 0000224433 5544444433 5555466663 5575566663 8877666663 8997777663 8999976666 ......*.*. .*.*...... .....*...* ...*...*.. .*...*.... .......*.* ..*.*..... *.......*. ..*...*... *...*..... 
valid 
Sample Input 2  Sample Output 2 

0000001111 0022221111 3322222111 3322222141 3355511144 3555516664 3771116664 7788811644 7888919944 7999999444 ......*.*. .*.*...... .....*...* ...*...*.. .*...*.... .......*.* ..*.*..... *.......*. ..*...*... *...*..... 
invalid 
Footnotes
 Star Battle puzzle images and test suite provided by krazydad.com, used with permission from author.