Jolly Jumpers..~

Problem Statement
     
NOTE: This problem statement contains images that may not display properly if viewed outside of the applet.  You are given a white rectangular grid made up of square cells. Some cells contain black squares, and some contain black squares that have been folded in half to form right triangles, such that one of their sides matches the grid line to the right of the cell and another side of the triangle matches the grid line to the bottom of the cell. At most unfoldLimit of these triangles can be unfolded to become black squares. However, black squares cannot be folded to become triangles.  We are interested in forming the largest possible proper black triangle in the grid using the aforementioned operations. A black triangle is considered proper within a grid configuration if no other black shape shares a line segment with it. However, black shapes may still share one or more points with the triangle. The size of a triangle is defined as the number of grid cells that are currently occupied by the triangle.  The grid will be given as a vector <string>, where the j-th character of the i-th element represents the cell at row i, column j. '.' represents an empty cell, '#' represents a cell containing a black square, and '/' represents a cell containing a black triangle. Return the largest possible size for a proper triangle that can be formed in the given grid by unfolding at most unfoldLimit triangles. In case it is not possible to form a proper black triangle in the grid, return -1.  For example, consider the following input grid:

Problem Statement
     
NOTE: This problem statement contains images that may not display properly if viewed outside of the applet.  "4Blocks" is a two player cooperative game played on a special board. The board is a grid composed of 1x1 square cells. There are two different kinds of blocks: '1' blocks and '4' blocks. '1' blocks are 1x1, and '4' blocks are 2x2:  

Problem Statement
     
It is a known fact that of all numbers, 4 is the one that brings the worst luck. It is for this reason that when generating number sequences, we need to avoid patterns related to the number 4 as much as possible.  You are given a long long n. Count the number of positive integers that satisfy all of the following conditions: 
The number contains at most n digits.
The number does not contain four consecutive '4' digits. For example, 43444124 is allowed, but 45444474 is not.
The number of digits in the number is not a multiple of any of the integers greater than 10 that contain only '4' in their decimal representations (44, 444, 4444, 44444, ...).
 Return the total count of these numbers modulo 1000000007.
Definition
   
Class:
AvoidFour
Method:
count
Parameters:
long long
Returns:
int
Method signature:
int count(long long n)
(be sure your method is public)
   
 
Constraints
-
n will be between 1 and 40000000000 (4e10), inclusive.
Examples
0)
 
   
4
Returns: 9998
Of all the 9999 positive integers containing 1, 2, 3 or 4 digits, 4444 is the only one that contains four consecutive '4' digits.
1)
 
   
5
Returns: 99980
The numbers to ignore are: 4444, 44440, 44441, 44442, ..., 44449, 14444, 24444, 34444, 54444, ... , 94444.
2)
 
   
87
Returns: 576334228
 
3)
 
   
88
Returns: 576334228
88 is a multiple of 44, so all numbers with 88 digits are ignored.
4)
 
   
4128
Returns: 547731225
 
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