Sigma Snake (WPC Style Puzzles #S1)

This Sigma Snake Puzzle type appeared in Oguz Atay Puzzle Contest(OAPC-1) championship. Can you solve this puzzle?

Instructions:

Draw a snake of letters in the grid, whose head and tail are given in circles and that doesn't touch itself, not even diagonally. Avoid grey cells with numbers. The snake must be formed only of numbers (as written in the given word list) in any order. A number on a grey cell gives the total of the adjacent (even at a point) numbers that are in the snake. You don't need to use all the words but you can use each word only once.

Number's Range:

One, Two, Three, Four, Five, Six, Seven, Eight, Nine