Given two circles: O1 with the center o1 = (x₁, y₁) and a radius r₁ and O2 with the center o2 = (x₂, y₂) and radius r₂, please compute if O1 is inside O2 or if O2 is inside O1.

Input

First t < 1000, the number of test cases. In each of the following t lines, 6 integers: x₁ y₁ r₁ x₂ y₂ r₂. Where 0 ≤ x₁, y₁, x₂, y₂ ≤ 10000 and 0 < r₁, r₂ ≤ 10000.

Output

For each test case print one character:

• I, if O1 is inside O2 (or if O2 is inside O1),
• E, if O1 is internally tangent to O2 (or if O2 is internally tangent to O1),
• O, in other cases.

Example

Input:
2
103 104 5 100 100 10
103 104 10 100 100 10

Output:
E
O