Area of Intersection between Two Circles

Write a program which prints the area of intersection between given circles $c1$ and $c2$.

Constraints

• $-10,000 \leq c1x, c1y, c2x, c2y \leq 10,000$
• $1 \leq c1r, c2r \leq 10,000$

Input

The input is given in the following format.

$c1x\; c1y\; c1r$ $c2x\; c2y\; c2r$

$c1x$, $c1y$ and $c1r$ represent the coordinate and radius of the first circle. $c2x$, $c2y$ and $c2r$ represent the coordinate and radius of the second circle. All input values are given in integers.

Output

Output the area in a line. The output values should be in a decimal fraction with an error less than 0.000001.

Examples

Input

0 0 1 2 0 2

Output

1.40306643968573875104

Input

1 0 1 0 0 3

Output

3.14159265358979311600

inputFormat

Input

The input is given in the following format.

$c1x\; c1y\; c1r$ $c2x\; c2y\; c2r$

$c1x$, $c1y$ and $c1r$ represent the coordinate and radius of the first circle. $c2x$, $c2y$ and $c2r$ represent the coordinate and radius of the second circle. All input values are given in integers.

outputFormat

Output

Output the area in a line. The output values should be in a decimal fraction with an error less than 0.000001.

Examples

Input

0 0 1 2 0 2

Output

1.40306643968573875104

Input

1 0 1 0 0 3

Output

3.14159265358979311600

样例

1 0 1
0 0 3

3.14159265358979311600