Advance Excel If Else Statement without VBA

Please bear with me here as this is going to be a bit long.

Objective: I'm trying to use If and Else statement without using VBA. I have 2013 Excel, therefore up to 64 IFs. I have a table consisting 7 rows and 14 columns (categorized in 7. Meaning each main column has 2 child columns. I've added an image with the formula I'm using).

Here are the conditions I'm trying to solve:

1. If there's any number in 'P' or 'R'for "Canada Only", then you don't have to input a number under "Canada & America only", "Canada & China only" or "Canada, America & China" column (for both 'P' or 'R').
2. If there's any number in 'P' or 'R'for "America Only", then you don't have to input a number under "Canada & America only", "America & China only" or "Canada, America & China" column.
3. If "Canada & America only" or "Canada & China only" or "Canada, America & China" have a value under either 'P' or 'R', then there does not need to be a value under 'P' or 'R' in "Canada only". (there just has to be one number despite which person does it in the row). This pattern applies to Canada, America and China.

My Approach:I tried to break it down. Important Note: I'm trying to add all the numbers that appear on the table (despite which row). So I work with the "Canada" scenario, where if any person inputs a value under "Canada only" then it sums of all the values on the table (and so there's no need to have a value under any country combinations that mention 'Canada' like "Canada and china only).

The best way to define is like this is an Auction/Bidding table, where each property should have a number attached to, regardless which person bid that number.

I hope i clarified the question properly.

The formula I used is:

IF(OR(B4>0,B5>0,B6>0,B7>0,B8>0,B9>0,B10>0),SUM(B4:C10),IF(OR(C4>0,C5>0,C6>0,C7>0,C8>0,C9>0,C10>0),SUM(B4:C10),"insert number"))

I tried coming up with one big IF formula, but I lose track very quickly, so I thought I break it down, and SUM the SUM of all of countries.

Excel Table IF Else Statement