The nth term of the sequence of triangle numbers is given by `t(n) = 0.5 * n(n+1)`; so the first ten triangle numbers are:

`1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...`

By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is `19 + 11 + 25 = 55 = t(10)`. If the word value is a triangle number then we shall call the word a triangle word.

Using words.txt (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common English words, how many are triangle words?
