Triangle Existence

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given three integer segment lengths $a,b,c$, determine whether they form a non-degenerate triangle. A degenerate arrangement is not a triangle.

Input

One line contains three integers $a,b,c$, the segment lengths.

Output

Print YES if a non-degenerate triangle can be formed, otherwise NO.

Subtasks

• Subtask 1 (20 points): Each length is between 0 and 10.

• Subtask 2 (30 points): Each length is between 0 and 1000.

• Subtask 3 (50 points): Each length is between 0 and 1,000,000.

Examples

Example 1

Input

3 4 5

Output

YES

Explanation

For this input, the case-specific computation and the required exact output are shown above. All three triangle inequalities hold strictly.

Example 2

Input

2 3 5

Output

NO

Explanation

For this input, the case-specific computation and the required exact output are shown above. The sum of the two short sides equals the longest side, so no triangle exists.