Petya bought a "Constructor" set, which contained 100 sticks of different lengths. The instructions for the "Constructor" state that any three sticks from the set can form a triangle. Petya decided to test this statement by forming triangles with the sticks. The sticks are arranged in the constructor in ascending order of length. What is the minimum number of checks (in the worst case) that Petya needs to perform to prove or disprove the statement in the instructions?
Pete only needs to check if it is possible to form a triangle from the two shortest sticks and the longest one. If the triangle cannot be formed, the statement in the instruction is refuted. If, however, the triangle can be formed, then the sum of the lengths of the two shortest sticks is greater than the length of the longest one. But in this case, the sum of the lengths of any two sticks in the set is longer than any other. (Indeed, the sum of the lengths of any two is no less than the sum of the lengths of the shortest, and the length of any stick is no greater than the length of the longest.) This means that a triangle can be formed from any sticks, i.e., the statement in the instruction is proven.

## Answer

One check