Let [a, b]=a b-a-b. Shaq sees the numbers 2,3, \ldots, 101 written on a blackboard. Let V be the largest number that Shaq can obtain by repeatedly choosing two numbers a, b on the board and replacing them with [a, b] until there is only one number left. Suppose N is the integer with N! nearest to V. Find the nearest integer to 10^6 \cdot \frac{|V-N!|}{N!}.