Problem: There are n cities along the road, which can be represented as a straight line. The i-th city is situated at the distance of a_i kilometers from the origin. All cities are situated in the same direction from the origin. There are m trucks travelling from one city to another. 

Each truck can be described by 4 integers: starting city s_i, finishing city f_i, fuel consumption c_i and number of possible refuelings r_i. The i-th truck will spend c_i litres of fuel per one kilometer. 

When a truck arrives in some city, it can be refueled (but refueling is impossible in the middle of nowhere). The i-th truck can be refueled at most r_i times. Each refueling makes truck's gas-tank full. All trucks start with full gas-tank.

All trucks will have gas-tanks of the same size V litres. You should find minimum possible V such that all trucks can reach their destinations without refueling more times than allowed.

Input

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

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 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 ≤ s_i < f_i ≤ n, 1 ≤ c_i ≤ 10^9, 0 ≤ r_i ≤ 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.

Example

Input


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


Output


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. 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int neck[400][400][401];
class Solution {
  int n, m;
  vector<int> a;

 public:
  void run(istream &in, ostream &out) {
    in >> n >> m;
    a.resize(n);
    for (int i = 0; i < n; ++i) in >> a[i];
    for (int s = 0; s < n; ++s) {
      for (int t = s; t < n; ++t) neck[s][t][0] = a[t] - a[s];
      for (int r = 1; r <= n; ++r) {
        int ts = s;
        for (int t = s + 1; t < n; ++t) {
          while (ts < t and max(neck[s][ts][r - 1], a[t] - a[ts]) >=
                                max(neck[s][ts + 1][r - 1], a[t] - a[ts + 1]))
            ++ts;
          neck[s][t][r] = max(neck[s][ts][r - 1], a[t] - a[ts]);
        }
      }
    }
    long long V = 0;
    for (int i = 0; i < m; ++i) {
      int f, s, c, r;
      in >> f >> s >> c >> r;
      --f, --s;
      V = max((long long)neck[f][s][r] * c, V);
    }
    out << V << '\n';
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  Solution().run(cin, cout);
}