No submission language available for this problem.

Description

Input

First line contains two integers $n$ and $m$ ($2 \le n \le 400$, $1 \le m \le 250000$) — the number of cities and trucks.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$, $a_i < a_{i+1}$) — positions of cities in the ascending order.

Next $m$ lines contains $4$ integers each. The $i$-th line contains integers $s_i$, $f_i$, $c_i$, $r_i$ ($1 \le s_i < f_i \le n$, $1 \le c_i \le 10^9$, $0 \le r_i \le n$) — the description of the $i$-th truck.

Output

Print the only integer — minimum possible size of gas-tanks $V$ such that all trucks can reach their destinations.

Samples

7 6
2 5 7 10 14 15 17
1 3 10 0
1 7 12 7
4 5 13 3
4 7 10 1
4 7 10 1
1 5 11 2

55

Note

Let's look at queries in details:

1. the $1$-st truck must arrive at position $7$ from $2$ without refuelling, so it needs gas-tank of volume at least $50$.
2. the $2$-nd truck must arrive at position $17$ from $2$ and can be refueled at any city (if it is on the path between starting point and ending point), so it needs gas-tank of volume at least $48$.
3. the $3$-rd truck must arrive at position $14$ from $10$, there is no city between, so it needs gas-tank of volume at least $52$.
4. the $4$-th truck must arrive at position $17$ from $10$ and can be refueled only one time: it's optimal to refuel at $5$-th city (position $14$) so it needs gas-tank of volume at least $40$.
5. the $5$-th truck has the same description, so it also needs gas-tank of volume at least $40$.
6. the $6$-th truck must arrive at position $14$ from $2$ and can be refueled two times: first time in city $2$ or $3$ and second time in city $4$ so it needs gas-tank of volume at least $55$.