The $n$^th term of the sequence of triangle numbers is given by, $t_n=\frac{1}{2}n(n+1)$; so the first ten triangle numbers are: $$1,3,6,10,15,21,28,36,45,55,\dots$$

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?