Telecorp

A robotic transporter shuttles between the factory and the laboratory of Telecorp, a company that builds teleporters. The factory and the laboratory lie on a straight road at distance $L$ km from each other — the factory at point $0$ and the laboratory at point $L$. The transporter starts at the factory and moves toward the laboratory at a speed of $1$ km per minute.

There are $N$ one-directional teleporters along the road. Teleporter $i$ sends the transporter from point $A_i$ to point $B_i$, where $A_i < B_i$. By themselves the teleporters cannot move the transporter, but Telecorp may install a module on any subset of them to activate them. There are $M$ module types available in unlimited supply.

When the transporter reaches an activated teleporter carrying module $j$, the teleportation instantly moves it from $A_i$ to $B_i$ and costs $C_j$ minutes measured at the transporter's current speed. Each module also recovers energy to accelerate the transporter: after passing through a teleporter with module $j$, the transporter permanently moves $V_j$ times faster. The speed-up compounds and applies to everything afterwards — both ordinary travel and any later teleportations become correspondingly faster.

Concretely, if the transporter's accumulated speed multiplier is $s$ (initially $s = 1$), then travelling a distance $d$ takes $d / s$ minutes, a teleportation with module $j$ takes $C_j / s$ minutes, and afterwards $s$ becomes $s \cdot V_j$.

The transporter never moves backward, so it may only use teleporters whose entry point lies at or ahead of its current position, and it may also pass any teleporter without using it. By choosing which teleporters to activate and which module to place on each, find the minimum possible time for the transporter to travel from the factory to the laboratory.

The first line contains three integers $N$, $M$, and $L$ ($1 \le N \le 10^5$, $1 \le M \le 10^5$, $1 \le L \le 10^9$): the number of teleporters, the number of module types, and the distance between the factory and the laboratory.

Each of the next $N$ lines contains two integers $A_i$ and $B_i$ ($0 \le A_i < B_i \le L$), meaning teleporter $i$ sends the transporter from point $A_i$ to point $B_i$.

Each of the last $M$ lines contains two real numbers $C_j$ and $V_j$ ($1 \le C_j \le 10^4$, $1 \le V_j \le 10^6$): with module $j$ a teleportation initially takes $C_j$ minutes and multiplies the transporter's speed by $V_j$.

Print a single number: the minimum time in minutes to travel from the factory to the laboratory, rounded to exactly three digits after the decimal point.