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This is a Korean CSAT mathematics numerical-answer problem. Solve it and put only the final integer value inside \boxed{}.
Problem 30 Ten empty boxes are arranged in a row, and there are eight balls. The balls are to be placed into the boxes so that no boxes are left unused, the total number of balls is 8, and each box contains at most two balls. (The balls are indistinguishable.) Find the number of such distributions that satisfy the following conditions. [4 points] (A) The number of boxes containing exactly one ball is either 4 or 6. (B) Any box containing two balls has empty neighboring boxes. Mathematics (Calculus)
\boxed{262}
Comparative Analysis (P29) (Average across runs)
Averages use reported measurements only. Missing usage is not treated as zero.