Problem: The only difference between easy and hard versions is a number of elements in the array.

You are given an array a consisting of n integers. The value of the i-th element of the array is a_i.

You are also given a set of m segments. The j-th segment is [l_j; r_j], where 1 ≤ l_j ≤ r_j ≤ n.

You can choose some subset of the given set of segments and decrease values on each of the chosen segments by one (independently). For example, if the initial array a = [0, 0, 0, 0, 0] and the given segments are [1; 3] and [2; 4] then you can choose both of them and the array will become b = [-1, -2, -2, -1, 0].

You have to choose some subset of the given segments (each segment can be chosen at most once) in such a way that if you apply this subset of segments to the array a and obtain the array b then the value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i will be maximum possible.

Note that you can choose the empty set.

If there are multiple answers, you can print any.

If you are Python programmer, consider using PyPy instead of Python when you submit your code.

Input

The first line of the input contains two integers n and m (1 ≤ n ≤ 300, 0 ≤ m ≤ 300) — the length of the array a and the number of segments, respectively.

The second line of the input contains n integers a_1, a_2, ..., a_n (-10^6 ≤ a_i ≤ 10^6), where a_i is the value of the i-th element of the array a.

The next m lines are contain two integers each. The j-th of them contains two integers l_j and r_j (1 ≤ l_j ≤ r_j ≤ n), where l_j and r_j are the ends of the j-th segment.

Output

In the first line of the output print one integer d — the maximum possible value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i if b is the array obtained by applying some subset of the given segments to the array a.

In the second line of the output print one integer q (0 ≤ q ≤ m) — the number of segments you apply.

In the third line print q distinct integers c_1, c_2, ..., c_q in any order (1 ≤ c_k ≤ m) — indices of segments you apply to the array a in such a way that the value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i of the obtained array b is maximum possible.

If there are multiple answers, you can print any.

Examples

Input


5 4
2 -2 3 1 2
1 3
4 5
2 5
1 3


Output


6
2
1 4 


Input


5 4
2 -2 3 1 4
3 5
3 4
2 4
2 5


Output


7
2
3 2 


Input


1 0
1000000


Output


0
0

Note

In the first example the obtained array b will be [0, -4, 1, 1, 2] so the answer is 6.

In the second example the obtained array b will be [2, -3, 1, -1, 4] so the answer is 7.

In the third example you cannot do anything so the answer is 0.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import static java.lang.Math.*;
import static java.util.Arrays.*;

public class Main {
	public static FastScanner in = new FastScanner();
	public static int []a;
	public static int[][]seg;
	public static int n,m;
	public static void main(String[] args) throws IOException {
		n=in.nextInt();
		m=in.nextInt();
		a=in.readArray(n);
		seg=new int[m][2];
		for(int i=0; i<m; ++i) {
			int L=in.nextInt(), R=in.nextInt();
			--L;
			--R;
			seg[i][0]=L;
			seg[i][1]=R;
		}
		int MAX=-IMAX;
		int pos=-1;
		for(int i=0; i<n; ++i) {
			int h=solve(i);
			if(h>MAX) {
				MAX=h;
				pos=i;
			}
		}
		//System.out.println(pos);
		System.out.println(MAX);
		ArrayList<Integer> ar=new ArrayList<Integer>();
		for(int i=0; i<m; ++i) {
			if(seg[i][0]>pos || seg[i][1]<pos) {
				ar.add(i+1);
			}
		}
		System.out.println(ar.size());
		for(int x:ar) System.out.print(x+" ");
		System.out.println();
		close();
	}
	
	static int solve(int t) {
		int ret=0;
		int []temp=new int[500];
		for(int i=0; i<n; ++i) {
			temp[i]=a[i];
		}
		for(int i=0; i<m; ++i) {
			if(seg[i][0]>t || seg[i][1]<t) {
				for(int j=seg[i][0]; j<=seg[i][1]; ++j) temp[j]--;
			}
		}
		int MIN=IMAX, MAX=IMIN;
		for(int i=0; i<n; ++i) {
			MAX=max(MAX,temp[i]);
			MIN=min(MIN,temp[i]);
		}
		return MAX-MIN;
	}

	static class FastScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");

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

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

		int[] readArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

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

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

	static BufferedReader __in = new BufferedReader(new InputStreamReader(System.in));
	static PrintWriter __out = new PrintWriter(new OutputStreamWriter(System.out));
	static StringTokenizer input;
	static Random __rand = new Random();

	// references
	// IBIG = 1e9 + 7
	// IMAX ~= 2e9
	// LMAX ~= 9e18

	// constants
	static final int IBIG = 1000000007;
	static final int IMAX = 2147483647;
	static final int IMIN = -2147483648;
	static final long LMAX = 9223372036854775807L;
	static final long LMIN = -9223372036854775808L;

	// math util
	static int minof(int a, int b, int c) {
		return min(a, min(b, c));
	}

	static int minof(int... x) {
		if (x.length == 1)
			return x[0];
		if (x.length == 2)
			return min(x[0], x[1]);
		if (x.length == 3)
			return min(x[0], min(x[1], x[2]));
		int min = x[0];
		for (int i = 1; i < x.length; ++i)
			if (x[i] < min)
				min = x[i];
		return min;
	}

	static long minof(long a, long b, long c) {
		return min(a, min(b, c));
	}

	static long minof(long... x) {
		if (x.length == 1)
			return x[0];
		if (x.length == 2)
			return min(x[0], x[1]);
		if (x.length == 3)
			return min(x[0], min(x[1], x[2]));
		long min = x[0];
		for (int i = 1; i < x.length; ++i)
			if (x[i] < min)
				min = x[i];
		return min;
	}

	static int maxof(int a, int b, int c) {
		return max(a, max(b, c));
	}

	static int maxof(int... x) {
		if (x.length == 1)
			return x[0];
		if (x.length == 2)
			return max(x[0], x[1]);
		if (x.length == 3)
			return max(x[0], max(x[1], x[2]));
		int max = x[0];
		for (int i = 1; i < x.length; ++i)
			if (x[i] > max)
				max = x[i];
		return max;
	}

	static long maxof(long a, long b, long c) {
		return max(a, max(b, c));
	}

	static long maxof(long... x) {
		if (x.length == 1)
			return x[0];
		if (x.length == 2)
			return max(x[0], x[1]);
		if (x.length == 3)
			return max(x[0], max(x[1], x[2]));
		long max = x[0];
		for (int i = 1; i < x.length; ++i)
			if (x[i] > max)
				max = x[i];
		return max;
	}

	static int powi(int a, int b) {
		if (a == 0)
			return 0;
		int ans = 1;
		while (b > 0) {
			if ((b & 1) > 0)
				ans *= a;
			a *= a;
			b >>= 1;
		}
		return ans;
	}

	static long powl(long a, int b) {
		if (a == 0)
			return 0;
		long ans = 1;
		while (b > 0) {
			if ((b & 1) > 0)
				ans *= a;
			a *= a;
			b >>= 1;
		}
		return ans;
	}

	static int fli(double d) {
		return (int) d;
	}

	static int cei(double d) {
		return (int) ceil(d);
	}

	static long fll(double d) {
		return (long) d;
	}

	static long cel(double d) {
		return (long) ceil(d);
	}

	static int gcf(int a, int b) {
		return b == 0 ? a : gcf(b, a % b);
	}

	static long gcf(long a, long b) {
		return b == 0 ? a : gcf(b, a % b);
	}

	static int lcm(int a, int b) {
		return a * b / gcf(a, b);
	}

	static long lcm(long a, long b) {
		return a * b / gcf(a, b);
	}

	static int randInt(int min, int max) {
		return __rand.nextInt(max - min + 1) + min;
	}

	static long hash(long x) {
		x += 0x9e3779b97f4a7c15L;
		x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L;
		x = (x ^ (x >> 27)) * 0x94d049bb133111ebL;
		return x ^ (x >> 31);
	}

	// array util
	static void reverse(int[] a) {
		for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
			int swap = a[i];
			a[i] = a[n - i - 1];
			a[n - i - 1] = swap;
		}
	}

	static void reverse(long[] a) {
		for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
			long swap = a[i];
			a[i] = a[n - i - 1];
			a[n - i - 1] = swap;
		}
	}

	static void reverse(char[] a) {
		for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
			char swap = a[i];
			a[i] = a[n - i - 1];
			a[n - i - 1] = swap;
		}
	}

	static void shuffle(int[] a) {
		int n = a.length - 1;
		for (int i = 0; i < n; ++i) {
			int ind = randInt(i, n);
			int swap = a[i];
			a[i] = a[ind];
			a[ind] = swap;
		}
	}

	static void shuffle(long[] a) {
		int n = a.length - 1;
		for (int i = 0; i < n; ++i) {
			int ind = randInt(i, n);
			long swap = a[i];
			a[i] = a[ind];
			a[ind] = swap;
		}
	}

	static void rsort(int[] a) {
		shuffle(a);
		sort(a);
	}

	static void rsort(long[] a) {
		shuffle(a);
		sort(a);
	}

	static int[] copy(int[] a) {
		int[] ans = new int[a.length];
		for (int i = 0; i < a.length; ++i)
			ans[i] = a[i];
		return ans;
	}

	static long[] copy(long[] a) {
		long[] ans = new long[a.length];
		for (int i = 0; i < a.length; ++i)
			ans[i] = a[i];
		return ans;
	}

	static char[] copy(char[] a) {
		char[] ans = new char[a.length];
		for (int i = 0; i < a.length; ++i)
			ans[i] = a[i];
		return ans;
	}

	// graph util
	static List<List<Integer>> g(int n) {
		List<List<Integer>> g = new ArrayList<>();
		for (int i = 0; i < n; ++i)
			g.add(new ArrayList<>());
		return g;
	}

	static List<Set<Integer>> sg(int n) {
		List<Set<Integer>> g = new ArrayList<>();
		for (int i = 0; i < n; ++i)
			g.add(new HashSet<>());
		return g;
	}

	static void c(List<? extends Collection<Integer>> g, int u, int v) {
		g.get(u).add(v);
		g.get(v).add(u);
	}

	static void cto(List<? extends Collection<Integer>> g, int u, int v) {
		g.get(u).add(v);
	}

	static void dc(List<? extends Collection<Integer>> g, int u, int v) {
		g.get(u).remove(v);
		g.get(v).remove(u);
	}

	static void dcto(List<? extends Collection<Integer>> g, int u, int v) {
		g.get(u).remove(v);
	}

	// input
	static void r() throws IOException {
		input = new StringTokenizer(__in.readLine());
	}

	static int ri() throws IOException {
		return Integer.parseInt(__in.readLine());
	}

	static long rl() throws IOException {
		return Long.parseLong(__in.readLine());
	}

	static int[] ria(int n) throws IOException {
		int[] a = new int[n];
		input = new StringTokenizer(__in.readLine());
		for (int i = 0; i < n; ++i)
			a[i] = Integer.parseInt(input.nextToken());
		return a;
	}

	static int[] riam1(int n) throws IOException {
		int[] a = new int[n];
		input = new StringTokenizer(__in.readLine());
		for (int i = 0; i < n; ++i)
			a[i] = Integer.parseInt(input.nextToken()) - 1;
		return a;
	}

	static long[] rla(int n) throws IOException {
		long[] a = new long[n];
		input = new StringTokenizer(__in.readLine());
		for (int i = 0; i < n; ++i)
			a[i] = Long.parseLong(input.nextToken());
		return a;
	}

	static char[] rcha() throws IOException {
		return __in.readLine().toCharArray();
	}

	static String rline() throws IOException {
		return __in.readLine();
	}

	static int rni() throws IOException {
		input = new StringTokenizer(__in.readLine());
		return Integer.parseInt(input.nextToken());
	}

	static int ni() {
		return Integer.parseInt(input.nextToken());
	}

	static long rnl() throws IOException {
		input = new StringTokenizer(__in.readLine());
		return Long.parseLong(input.nextToken());
	}

	static long nl() {
		return Long.parseLong(input.nextToken());
	}

	static List<List<Integer>> rg(int n, int m) throws IOException {
		List<List<Integer>> g = g(n);
		for (int i = 0; i < m; ++i)
			c(g, rni() - 1, ni() - 1);
		return g;
	}

	static void rg(List<List<Integer>> g, int m) throws IOException {
		for (int i = 0; i < m; ++i)
			c(g, rni() - 1, ni() - 1);
	}

	static List<List<Integer>> rdg(int n, int m) throws IOException {
		List<List<Integer>> g = g(n);
		for (int i = 0; i < m; ++i)
			cto(g, rni() - 1, ni() - 1);
		return g;
	}

	static void rdg(List<List<Integer>> g, int m) throws IOException {
		for (int i = 0; i < m; ++i)
			cto(g, rni() - 1, ni() - 1);
	}

	static List<Set<Integer>> rsg(int n, int m) throws IOException {
		List<Set<Integer>> g = sg(n);
		for (int i = 0; i < m; ++i)
			c(g, rni() - 1, ni() - 1);
		return g;
	}

	static void rsg(List<Set<Integer>> g, int m) throws IOException {
		for (int i = 0; i < m; ++i)
			c(g, rni() - 1, ni() - 1);
	}

	static List<Set<Integer>> rdsg(int n, int m) throws IOException {
		List<Set<Integer>> g = sg(n);
		for (int i = 0; i < m; ++i)
			cto(g, rni() - 1, ni() - 1);
		return g;
	}

	static void rdsg(List<Set<Integer>> g, int m) throws IOException {
		for (int i = 0; i < m; ++i)
			cto(g, rni() - 1, ni() - 1);
	}

	// output
	static void pr(int i) {
		__out.print(i);
	}

	static void prln(int i) {
		__out.println(i);
	}

	static void pr(long l) {
		__out.print(l);
	}

	static void prln(long l) {
		__out.println(l);
	}

	static void pr(double d) {
		__out.print(d);
	}

	static void prln(double d) {
		__out.println(d);
	}

	static void pr(char c) {
		__out.print(c);
	}

	static void prln(char c) {
		__out.println(c);
	}

	static void pr(char[] s) {
		__out.print(new String(s));
	}

	static void prln(char[] s) {
		__out.println(new String(s));
	}

	static void pr(String s) {
		__out.print(s);
	}

	static void prln(String s) {
		__out.println(s);
	}

	static void pr(Object o) {
		__out.print(o);
	}

	static void prln(Object o) {
		__out.println(o);
	}

	static void prln() {
		__out.println();
	}

	static void pryes() {
		__out.println("yes");
	}

	static void pry() {
		__out.println("Yes");
	}

	static void prY() {
		__out.println("YES");
	}

	static void prno() {
		__out.println("no");
	}

	static void prn() {
		__out.println("No");
	}

	static void prN() {
		__out.println("NO");
	}

	static void pryesno(boolean b) {
		__out.println(b ? "yes" : "no");
	};

	static void pryn(boolean b) {
		__out.println(b ? "Yes" : "No");
	}

	static void prYN(boolean b) {
		__out.println(b ? "YES" : "NO");
	}

	static void prln(int... a) {
		for (int i = 0, len = a.length - 1; i < len; __out.print(a[i]), __out.print(' '), ++i)
			;
		__out.println(a[a.length - 1]);
	}

	static void prln(long... a) {
		for (int i = 0, len = a.length - 1; i < len; __out.print(a[i]), __out.print(' '), ++i)
			;
		__out.println(a[a.length - 1]);
	}

	static <T> void prln(Collection<T> c) {
		int n = c.size() - 1;
		Iterator<T> iter = c.iterator();
		for (int i = 0; i < n; __out.print(iter.next()), __out.print(' '), ++i)
			;
		if (n >= 0)
			__out.println(iter.next());
		else
			__out.println();
	}

	static void h() {
		__out.println("hlfd");
		flush();
	}

	static void flush() {
		__out.flush();
	}

	static void close() {
		__out.close();
	}
}