Triangle Classification by Sides

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given integer lengths $a,b,c$, first determine if they form a non-degenerate triangle. If valid, classify by side equality as equilateral, isosceles (exactly two equal), or scalene.

Input

A line contains three integers $a,b,c$.

Output

Print one of INVALID, EQUILATERAL, ISOSCELES, or SCALENE.

Subtasks

• Subtask 1 (20 points): All lengths are in [0,10].

• Subtask 2 (30 points): All lengths are in [0,1000].

• Subtask 3 (50 points): All lengths are in [0,1,000,000].

Examples

Example 1

Input

5 5 5

Output

EQUILATERAL

Explanation

For this input, the case-specific computation and the required exact output are shown above. All sides are equal in a valid triangle.

Example 2

Input

1 2 3

Output

INVALID

Explanation

For this input, the case-specific computation and the required exact output are shown above. The three lengths fail the strict triangle inequality.