Problem: Vasya plays one very well-known and extremely popular MMORPG game. His game character has k skill; currently the i-th of them equals to ai. Also this game has a common rating table in which the participants are ranked according to the product of all the skills of a hero in the descending order.

Vasya decided to 'upgrade' his character via the game store. This store offers n possible ways to improve the hero's skills; Each of these ways belongs to one of three types:

  1. assign the i-th skill to b; 
  2. add b to the i-th skill; 
  3. multiply the i-th skill by b. 



Unfortunately, a) every improvement can only be used once; b) the money on Vasya's card is enough only to purchase not more than m of the n improvements. Help Vasya to reach the highest ranking in the game. To do this tell Vasya which of improvements he has to purchase and in what order he should use them to make his rating become as high as possible. If there are several ways to achieve it, print any of them.

Input

The first line contains three numbers — k, n, m (1 ≤ k ≤ 105, 0 ≤ m ≤ n ≤ 105) — the number of skills, the number of improvements on sale and the number of them Vasya can afford.

The second line contains k space-separated numbers ai (1 ≤ ai ≤ 106), the initial values of skills.

Next n lines contain 3 space-separated numbers tj, ij, bj (1 ≤ tj ≤ 3, 1 ≤ ij ≤ k, 1 ≤ bj ≤ 106) — the type of the j-th improvement (1 for assigning, 2 for adding, 3 for multiplying), the skill to which it can be applied and the value of b for this improvement.

Output

The first line should contain a number l (0 ≤ l ≤ m) — the number of improvements you should use.

The second line should contain l distinct space-separated numbers vi (1 ≤ vi ≤ n) — the indices of improvements in the order in which they should be applied. The improvements are numbered starting from 1, in the order in which they appear in the input. 

Examples

Input

2 4 3
13 20
1 1 14
1 2 30
2 1 6
3 2 2


Output

3
2 3 4

Solution (in JAVA):

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

public class D {

	BufferedReader br;
	PrintWriter out;
	StringTokenizer st;
	boolean eof;

	static class Item implements Comparable<Item> {
		int type, delta, id;

		@Override
		public int compareTo(Item o) {
			return -Integer.compare(delta, o.delta);
		}

		public Item(int type, int delta, int id) {
			this.type = type;
			this.delta = delta;
			this.id = id;
		}
	}

	static class Profit implements Comparable<Profit> {
		Item item;
		long num, denom;

		public Profit(Item item, long num, long denom) {
			this.item = item;
			this.num = num;
			this.denom = denom;
		}

		@Override
		public int compareTo(Profit o) {
			// num/denom > o.num/o.denom -> -1
			long v1 = num * o.denom;
			long v2 = o.num * denom;
			return -Long.compare(v1, v2);
		}
	}

	void solve() throws IOException {
		int k = nextInt();
		int n = nextInt();
		int take = nextInt();
		int[] a = new int[k];
		for (int i = 0; i < k; i++) {
			a[i] = nextInt();
		}

		List<Item>[][] b = new List[k][3];
		for (int i = 0; i < k; i++) {
			for (int j = 0; j < 3; j++) {
				b[i][j] = new ArrayList<>(0);
			}
		}

		for (int i = 0; i < n; i++) {
			int type = nextInt() - 1;
			int where = nextInt() - 1;
			int delta = nextInt();
			b[where][type].add(new Item(type, delta, i));
		}

		List<Profit> pr = new ArrayList<>(n);

		for (int i = 0; i < k; i++) {
			List<Item>[] bi = b[i];
			for (int j = 0; j < 3; j++) {
				Collections.sort(bi[j]);
			}
			if (!bi[0].isEmpty()) {
				int add = bi[0].get(0).delta - a[i];
				if (add > 0) {
					bi[1].add(new Item(0, add, bi[0].get(0).id));
					Collections.sort(bi[1]);
				}
			}

			long curA = a[i];
			for (Item it : bi[1]) {
				pr.add(new Profit(it, curA + it.delta, curA));
				curA += it.delta;
			}
			for (Item it : bi[2]) {
				if (it.delta != 1) {
					pr.add(new Profit(it, it.delta, 1));
				}
			}

		}

		Collections.sort(pr);
		List<Item> answer = new ArrayList<>(take);
		for (int i = 0; i < take && i < pr.size(); i++) {
			answer.add(pr.get(i).item);
		}
		Collections.sort(answer, new Comparator<Item>() { // this shit better be
															// stable

					@Override
					public int compare(Item o1, Item o2) {
						return Integer.compare(o1.type, o2.type);
					}
				});
		out.println(answer.size());
		for (Item it : answer) {
			out.print(it.id + 1 + " ");
		}
		out.println();
	}

	D() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	public static void main(String[] args) throws IOException {
		new D();
	}

	String nextToken() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (Exception e) {
				eof = true;
				return null;
			}
		}
		return st.nextToken();
	}

	String nextString() {
		try {
			return br.readLine();
		} catch (IOException e) {
			eof = true;
			return null;
		}
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}