Putnik

Huge numbers of people ride commuter trains every day. This problem covers the line from the station "Zhilye Mytishchi" (ZhM for short) to the station "Bolshaya Tsentralnaya" (BTs for short). The line has $n + 1$ stations. Station ZhM has number $n$, and station BTs has number $0$. Stations $i$ and $i + 1$ are connected by a track segment for every $i$, and no other pairs of stations are connected. Every train starts at ZhM and goes to BTs. Station $i$ has $c_i$ passengers each day who want to reach BTs, and there are no other passengers. An ordinary train needs $e_i$ minutes to cover the segment between station $i$ and station $i - 1$. Passengers board instantly. The board of directors has decided to run an express from the ZhM depot to BTs. The new train is called "Putnik". Each segment has its own track for Putnik, and it takes Putnik $p_i$ minutes to travel from station $i$ to station $i - 1$. As often happens in practice, $p_i$ can be less than $e_i$ or greater than it. Putnik is an express, so each stop takes one minute for the attendants to give a safety briefing on high-speed trains. Passengers follow a simple rule. They switch to the new express only if it makes their travel time from their station to station $0$ strictly smaller. A passenger boards Putnik at the very start of its stop, so the passenger spends that minute on the greeting and the briefing. The board wants to maximize the number of people who ride the new train. Choose the stations where the express stops so that as many people as possible ride it. Putnik starts from the ZhM depot, but it does not have to stop at ZhM.

The first line contains $n$ ($1 \leq n \leq 1000$), the number of segments between ZhM and BTs. The second line contains $n$ integers $e_i$ ($1 \leq e_i \leq 10^9$), the minutes an ordinary train needs to travel from station $i$ to station $i - 1$. The third line contains $n$ integers $c_i$ ($1 \leq c_i \leq 10^9$), the number of people each day who try to get from station $i$ to station $0$. The fourth line contains $n$ integers $p_i$ ($1 \leq p_i \leq 10^9$), the minutes Putnik needs to travel the segment between stations $i$ and $i - 1$.

Print one integer, the maximum possible number of passengers who ride the new express.

In the first sample, Putnik reaches BTs one minute faster than the ordinary train if it makes no stops. However, if it stops anywhere, that advantage disappears and nobody rides the new train. In the second sample, the express must stop at stations $2$ and $3$. It cannot stop at station $1$, because that would make the trips from station $2$ unprofitable.