Broken Vending Machine

Bob found a vending machine that is broken, and he wants to make money from it. The machine has $n$ positions, numbered 1 to $n$. Position $i$ holds $s_i$ snacks, one press of its button costs $p_i$, and one snack from that position sells on the market for $m_i$.

The machine is broken in a consistent way. When Bob presses the button at position $i$, the machine charges him $p_i$ and then dispenses one snack from position $f(i)$ instead of position $i$. If position $f(i)$ is already empty, Bob pays and receives nothing. A press at position $i$ never reduces the number of snacks at position $i$; only the position the snack came out of loses one. Bob may press any button as many times as he likes, in any order, and he pays for every press.

Bob sells every snack he receives at its market price, and a snack that came out of position $j$ sells for $m_j$. He has enough money to pay for any number of presses. Find the largest net gain Bob can reach, that is, the total market price of the snacks he receives minus the total amount he pays. Pressing nothing at all is allowed.

The first line contains the number of positions $n$ ($1 \le n \le 10^5$). Each of the next $n$ lines describes one position, from position 1 to position $n$, with four integers $f$, $p$, $m$, $s$.

• $f$ is the position $f(i)$ the machine dispenses from when Bob presses this position's button ($1 \le f \le n$).
• $p$ is the price of one press at this position ($1 \le p \le 10^6$).
• $m$ is the market price of a snack at this position ($1 \le m \le 10^6$).
• $s$ is the number of snacks at this position ($1 \le s \le 10^6$).

Print the largest net gain Bob can reach as a single integer on one line.