Given a string consist just of the letter 'u' ,if we can consider every two adjacent 'u' -->' w' and every u can be used only once in how many ways the string can appear ?

example : uuu can be uuu or wu or u w so the answer is 3 .

I am asking this question because at the last contest I was trying to solve this problem https://codeforces.net/contest/1245/problem/C and I claim the solution is every continuous 'u' or 'n' I save in how many ways it can appear in a vector and then multiply all the numbers and this is the answer .