Important targets

Limits: 1 sec., 256 MiB

This statement was translated automatically from Ukrainian.

The Main Directorate of Intelligence learned about three large enemy equipment bases. Their coordinates are \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\).

Zenyk was tasked with planning a special operation to destroy these targets.

To carry out the operation, the GUR can allocate to Zenyk at most three missiles with the same destruction radius. The destruction zone of a missile with a destruction radius \(R\) that hits the point \((x, y)\) is a circle of radius \(R\) centered at this point. A missile destroys all targets located inside its destruction zone. The destruction zone of the attack is defined as the union of the destruction zones of the missiles launched within this attack.

Zenyk needs to find out what minimum missile destruction radius he needs in order to achieve both goals of the special operation:

1. Destroy all three enemy bases.

2. Ensure the integrity of the attack’s destruction zone. That is, between every two hit points there must exist a path that passes within the destruction zone.

Input

The first three lines each contain two integers \(x_i\), \(y_i\) — the coordinates of the corresponding target.

Output

In a single line, output a single number — the minimum missile destruction radius that will satisfy both goals of the special operation.

The answer will be considered correct if the absolute or relative error does not exceed \(10^{-7}\).

Constraints

\(-1000 \le x_i, y_i \le 1000\),

if \(i \ne j\), then \((x_i, y_i) \ne (x_j, y_j)\) — no points coincide.

In at least five tests, the input points lie on the same line.

Samples

Input (stdin) сopy	Output (stdout) сopy
0 0 3 4 3 -2	1.25

Input (stdin) сopy	Output (stdout) сopy
0 0 0 1 0 6	1

Notes