Problem: Malek is a rich man. He also is very generous. That's why he decided to split his money between poor people. A charity institute knows n poor people numbered from 1 to n. The institute gave Malek q recommendations. A recommendation is a segment of people like [l, r] which means the institute recommended that Malek gives one dollar to every person whose number is in this segment.

However this charity has very odd rules about the recommendations. Because of those rules the recommendations are given in such a way that for every two recommendation [a, b] and [c, d] one of the following conditions holds: 

  * The two segments are completely disjoint. More formally either a ≤ b < c ≤ d or c ≤ d < a ≤ b
  * One of the two segments are inside another. More formally either a ≤ c ≤ d ≤ b or c ≤ a ≤ b ≤ d. 



The goodness of a charity is the value of maximum money a person has after Malek finishes giving his money. The institute knows for each recommendation what is the probability that Malek will accept it. They want to know the expected value of goodness of this charity. So they asked you for help.

You have been given the list of recommendations and for each recommendation the probability of it being accepted by Malek. You have also been given how much money each person initially has. You must find the expected value of goodness.

Input

In the first line two space-separated integers n, q (1 ≤ n ≤ 105, 1 ≤ q ≤ 5000) are given.

In the second line n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 109) are given meaning that person number i initially has ai dollars. 

Each of the next q lines contains three space-separated numbers li, ri, pi (1 ≤ li ≤ ri ≤ n, 0 ≤ p ≤ 1) where li and ri are two integers describing the segment of recommendation and pi is a real number given with exactly three digits after decimal point which is equal to probability of Malek accepting this recommendation.

Note that a segment may appear several times in recommendations.

Output

Output the sought value. Your answer will be considered correct if its absolute or relative error is less than 10 - 6.

Examples

Input

5 2
1 7 2 4 3
1 3 0.500
2 2 0.500


Output

8.000000000


Input

5 2
281 280 279 278 282
1 4 1.000
1 4 0.000


Output

282.000000000


Input

3 5
1 2 3
1 3 0.500
2 2 0.250
1 2 0.800
1 1 0.120
2 2 0.900


Output

4.465000000

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class CF {
	FastScanner in;
	PrintWriter out;

	final int MAX = 5003;

	class Obj implements Comparable<Obj> {
		int minValue;
		int left;
		double[] pr;

		public Obj(int minValue, int left) {
			super();
			this.minValue = minValue;
			this.left = left;
		}

		@Override
		public int compareTo(Obj o) {
			if (left == o.left)
				return Integer.compare(minValue, o.minValue);
			return Integer.compare(left, o.left);
		}

		@Override
		public String toString() {
			return "Obj [minValue=" + minValue + ", left=" + left + ", pr="
					+ Arrays.toString(pr) + "]";
		}

	}

	class Q implements Comparable<Q> {
		int left, right;
		double pr;

		public Q(int left, int right, double pr) {
			super();
			this.left = left;
			this.right = right;
			this.pr = pr;
		}

		@Override
		public int compareTo(Q o) {
			return Integer.compare(right - left, o.right - o.left);
		}

		@Override
		public String toString() {
			return "Q [left=" + left + ", right=" + right + ", pr=" + pr + "]";
		}

	}

	void solve() {
		int n = in.nextInt();
		int q = in.nextInt();
		int[] a = new int[n];
		TreeSet<Obj> all = new TreeSet<>();
		for (int i = 0; i < n; i++) {
			a[i] = in.nextInt();
			all.add(new Obj(a[i], i));
		}
		Q[] qu = new Q[q + 1];
		for (int i = 0; i < q; i++) {
			qu[i] = new Q(in.nextInt() - 1, in.nextInt() - 1, in.nextDouble());
		}
		qu[q] = new Q(0, n - 1, 0.0);
		Arrays.sort(qu);
		for (Q curQ : qu) {
			ArrayList<Obj> inside = new ArrayList<>();
			int minVal = -1;
			while (true) {
				Obj o = all.higher(new Obj(-1, curQ.left));
				if (o == null) {
					break;
				}
				if (o.left <= curQ.right) {
					if (o.pr == null) {
						minVal = Math.max(minVal, o.minValue);
					} else {
						inside.add(o);
					}
					all.remove(o);
				} else {
					break;
				}
			}
			for (Obj o : inside) {
				minVal = Math.max(minVal, o.minValue);
			}
			Obj newObj = new Obj(minVal, curQ.left);
			newObj.pr = new double[MAX];
			double[] curSub = new double[inside.size()];
			double cursum = 0;
			for (int i = MAX - 1; i > 0; i--) {
				double prNot = 1.0;
				for (int j = 0; j < inside.size(); j++) {
					int need = minVal + i;
					int id = need - inside.get(j).minValue;
					if (id >= 0 && id < MAX) {
						double curP = inside.get(j).pr[id] + curSub[j];
						curSub[j] = curP;
						prNot *= 1 - curP;
					}
				}
				newObj.pr[i] = 1 - prNot - cursum;
				cursum += newObj.pr[i];
			}
			double sum = 1;
			for (int i = 1; i < MAX; i++) {
				sum -= newObj.pr[i];
			}
			newObj.pr[0] = sum;
			for (int i = MAX - 1; i > 0; i--) {
				newObj.pr[i] += newObj.pr[i - 1] * curQ.pr;
				newObj.pr[i - 1] = newObj.pr[i - 1] * (1 - curQ.pr);
			}
			all.add(newObj);
		}
		Obj o = all.first();
		double result = 0;
		for (int i = 0; i < MAX; i++) {
			result += o.pr[i] * (o.minValue + i);
		}
		out.println(result);
	}

	void runIO() {

		in = new FastScanner(System.in);
		out = new PrintWriter(System.out);

		solve();

		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		public FastScanner(InputStream f) {
			br = new BufferedReader(new InputStreamReader(f));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (s == null)
					return null;
				st = new StringTokenizer(s);
			}
			return st.nextToken();
		}

		boolean hasMoreTokens() {
			while (st == null || !st.hasMoreTokens()) {
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (s == null)
					return false;
				st = new StringTokenizer(s);
			}
			return true;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}
	}

	public static void main(String[] args) {
		new CF().runIO();
	}
}