**Problem Description**

The route is a straight line, some of which is directly burned by the sun, while some are in the shade.

Xiaoxi’s walking speed is 1/s, which does not cost energy.

The total length of the path is S. There are N disjoint interval (l, r), which indicated the part [l, r] are in the shade. XiaoXi starts with C unit of energy. She can cost 1 unit of energy per second to walk faster for a while, and in this case, she could get a 2/s movement speed during this time. She can also cost 3 unit of energy per second to run for a while, so that she can get 3/s of movement speed during this time.

Note: time is continuous. For example, XiaoXi can spend 2 unit energy to run for 2/3 seconds.

Xiaoxi can decide her way of moving at any time. She hopes to be exposed to the sun for the shortest time.

**Input**

The first line contains an integer T specifying the number of test cases.

Each test case firstly consists of a single line containing three integers S, N and C, in which s is the length of the route, and N is the number of the disjoint interval and C is the Initial energy of Xiaoxi.

The next N lines each contains two integers l and r , describe the part [l, r] is covered.

T<=1000

S, l, r, C<= 1000000000

N <= 1000

l <= r , l

_{i}<=l

_{i}+1

**Output**

Output the minimum time of which XiaoXi burned by the sun (Round to 6 decimal places)

**Sample Input**

3 100 0 10 100 2 20 10 20 60 100 100 1 100 0 90

**Sample Output**

90.000000 30.000000 3.333333

**Source**

2018市赛