Parabolic Teleports

Flatland is a plane with a Cartesian coordinate system $Oxy$. Its citizens are points that move at speed $1$, so the minimum time to travel from a point $V$ to a point $W$ equals the length of the segment $VW$. Flatland schools teach this as the "shortest path theorem".

The theorem stopped holding once parabolic teleports were invented. A parabolic teleport is a contiguous arc of a parabola along which you can move at infinite speed: you can travel between any two points on the same teleport in zero time.

The points $(x, y)$ of a teleport satisfy $y = A x^2 + B x + C$ for $X_L \le x \le X_R$, where $A$, $B$, $C$, $X_L$, $X_R$ are the teleport's parameters.

$N$ teleports have already been built. Given two points $V$ and $W$, compute the minimum time needed to travel from $V$ to $W$. You may walk in a straight line between any two points at speed $1$, and you may step onto or off of any teleport at any of its points at no cost.

The first line contains an integer $N$ ($0 \le N \le 100$), the number of teleports. The second line contains two integers $X_V$ and $Y_V$ ($-100 \le X_V \le 100$, $-10^6 \le Y_V \le 10^6$), the coordinates of the source point $V$. The third line contains two integers $X_W$ and $Y_W$ ($-100 \le X_W \le 100$, $-10^6 \le Y_W \le 10^6$), the coordinates of the destination point $W$.

Each of the next $N$ lines contains five integers $A_i$, $B_i$, $C_i$, $X_{Li}$, $X_{Ri}$ describing the $i$-th teleport ($-100 \le A_i, B_i, C_i \le 100$, $A_i \ne 0$, $-100 \le X_{Li} < X_{Ri} \le 100$).

Print a single number: the minimum time to travel from $V$ to $W$, rounded to exactly $4$ digits after the decimal point.