Problem: Polycarp is in really serious trouble — his house is on fire! It's time to save the most valuable items. Polycarp estimated that it would take ti seconds to save i-th item. In addition, for each item, he estimated the value of di — the moment after which the item i will be completely burned and will no longer be valuable for him at all. In particular, if ti ≥ di, then i-th item cannot be saved.

Given the values pi for each of the items, find a set of items that Polycarp can save such that the total value of this items is maximum possible. Polycarp saves the items one after another. For example, if he takes item a first, and then item b, then the item a will be saved in ta seconds, and the item b — in ta + tb seconds after fire started.

Input

The first line contains a single integer n (1 ≤ n ≤ 100) — the number of items in Polycarp's house.

Each of the following n lines contains three integers ti, di, pi (1 ≤ ti ≤ 20, 1 ≤ di ≤ 2 000, 1 ≤ pi ≤ 20) — the time needed to save the item i, the time after which the item i will burn completely and the value of item i.

Output

In the first line print the maximum possible total value of the set of saved items. In the second line print one integer m — the number of items in the desired set. In the third line print m distinct integers — numbers of the saved items in the order Polycarp saves them. Items are 1-indexed in the same order in which they appear in the input. If there are several answers, print any of them.

Examples

Input

3
3 7 4
2 6 5
3 7 6


Output

11
2
2 3 


Input

2
5 6 1
3 3 5


Output

1
1
1 

Note

In the first example Polycarp will have time to save any two items, but in order to maximize the total value of the saved items, he must save the second and the third item. For example, he can firstly save the third item in 3 seconds, and then save the second item in another 2 seconds. Thus, the total value of the saved items will be 6 + 5 = 11.

In the second example Polycarp can save only the first item, since even if he immediately starts saving the second item, he can save it in 3 seconds, but this item will already be completely burned by this time.

Solution (in JAVA):

Solution:
	import java.io.*;
	import java.util.*;
	
	public class Main
	{
		private InputStream is;
		private PrintWriter out;
		int time = 0, DP[], start[], end[], dist[], black[], MOD = (int) (1e9 + 7),
				arr[], weight[][], x[], y[], parent[];
		int MAX = 100010, N, K;
		long red[],ans = Long.MAX_VALUE;
		
		ArrayList<Character>[] amp;
		ArrayList<Pair>[] pmp;
		boolean b[], boo[][], b1[];
		Pair prr[];
		HashMap<Pair, Integer> hm = new HashMap();
		long Dp[][][][] = new long[110][110][12][12];
		void soln()
		{
			is = System.in;
			out = new PrintWriter(System.out);
			long s = System.currentTimeMillis();
			solve();
			
			// out.close();
			out.flush();
			// tr(System.currentTimeMillis() - s + "ms");
		}
		static class ST1 //min ST
		{
			long arr[], st[];
			int size;
	
			
			ST1(long a[]) 
			{
				arr = a.clone();
				size = 10 * arr.length;
				st = new long[size];
				build(0, arr.length - 1, 1);
			}
	
			void build(int ss, int se, int si) 
			{
				if (ss == se)
				{
					st[si] = arr[ss];
					return;
				}
				int mid = (ss + se) / 2;
				int val = 2 * si;
				build(ss, mid, val);
				build(mid + 1, se, val + 1);
				st[si] = Math.min(st[val], st[val + 1]);
			}
			void update(int ss, int se, int idx, long val, int si) {
				if(ss==se) {
					//if(si==idx+1)
					st[si] = val;
					return;
				}				
				int mid = (ss+se)/2;
				if(ss<=idx && idx<=mid) {
					update(ss,mid,idx,val,2*si);
				}
				else {
					update(mid+1, se, idx, val, 2*si+1);
				}
				int v = 2*si;
				st[si] = Math.min(st[v], st[v + 1]);
			}
			long get(int ss, int se, int l, int r, int si) 
			{
				if (l > se || r < ss || l > r)
					return Long.MAX_VALUE/1000;
				if (l <= ss && r >= se)
					return st[si];
				int mid = (ss + se) / 2;
				int val = 2 * si;
				return Math.min(get(ss, mid, l, r, val),
						get(mid + 1, se, l, r, val + 1));
			}
		}
		public static void main(String[] args) throws Exception 
		{
			new Thread(null, new Runnable() 
			{
				public void run() 
				{
					try
					{
						// new CODEFORCES().soln();
					} catch (Exception e)
					{
						System.out.println(e);
					}
				}
			}, "1", 1 << 26).start();
			new Main().soln();
		}
	
		int  cost = 0, D[][];
		char ch[], ch1[];
		int hash = 29;
		//TreeSet<Cell> ts;
		int x2, y2;
		HashSet<Integer>[] hs = (HashSet<Integer>[]) new HashSet[110];
		cell[] c;
		void solve(){
			int n = ni();
			N = n;
			c = new cell[n];
			for(int i = 0; i< n; i++) {
				c[i] = new cell(ni(),ni(),ni(),i);
			}
			D = new int[n][3000];
			for(int i = 0; i< n; i++) Arrays.fill(D[i], -1);
			Arrays.sort(c);
			System.out.println(recur(0,0));
			int val = D[0][0], time = 0;
			ArrayList<Integer> amp = new ArrayList<>();
			for(int i=0;i<n-1;i++) {
				if(D[i+1][time]!=val) {
					amp.add(c[i].i+1);
					time += c[i].t;
					val-=c[i].p;
				}
			}
			if(D[n-1][time]>0) amp.add(c[n-1].i+1);
			System.out.println(amp.size());
			for(int i : amp) System.out.print(i+" ");
		}
		int recur(int i, int time) {
			if(i>=N) return 0;
			if(D[i][time]!=-1) return D[i][time];
			if((time+c[i].t)>=c[i].d) return D[i][time] = recur(i+1,time);
			return D[i][time] = max(recur(i+1,time),c[i].p+recur(i+1,time+c[i].t));
		}
		static class cell implements Comparable<cell>{
			int t,d,p,i;
			cell(int t, int d, int p ,int i){
				this.t = t;
				this.p = p;
				this.d = d;
				this.i = i;
			}
			public int compareTo(cell other)
			{
				// return Integer.compare(val, other.val);
				return Long.compare(d, other.d);// != 0 ? (Long.compare(d, other.u)): (Long.compare(v, other.v));//((Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)): (Long.compare(v, other.v)))
						//&(Long.compare(u, other.v) != 0 ? (Long.compare(u, other.v)): (Long.compare(v, other.u))));
			}
			public String toString()
			{
				return this.d + " " + this.t;
			}
		}
		long abs(long x) {
			return ((x>0)?x:-x);
		}
		long ret(int p) {
			if(p>=0) return 0;
			else return 1;
		}
		long val(int p,int a, int b) {
			if(p>=0) {
				return (a*1l*p);
			}
			return (b*1l*p);
		}
		void ternary_search(int l,int r)
		{ 
			//System.out.println(l+" "+r+" "+ans);
		//	for(int i : arr) System.out.print(i+" ");
		//	System.out.println();
		    if(r>=l)
		    {
		        int mid1 = l + (r-l)/3;
		        int mid2 = r -  (r-l)/3;
		        long cnt1 = 0, cnt2 = 0;
		        cnt1 = compute(mid1);
		        cnt2 = compute(mid2);
		       // System.out.println(mid1+" "+ cnt1+" "+mid2+" "+cnt2);
		        ans = Math.min(cnt1,cnt2);
		        if(cnt1<cnt2){
		        	ternary_search(l, mid2-1);
		        }
		        else{
		        	ternary_search(mid1+1, r);
		        }
		    }
		    return;
		}
		long compute(int x){
			long ans = 0;
			int c = arr[0];
			for(int i = 1; i<=x;i++){
				ans += max(c+1-arr[i],0);
				c = max(c+1,arr[i]);
			}
			int temp = arr[x];
			arr[x] = max(c+1,arr[x]);
			//SSystem.out.println(arr[x]+" "+ans);
			c = arr[arr.length-1];
			for(int i = arr.length-1;i>x;i--){
				ans += max(c+1-arr[i-1],0);
				c = max(c+1,arr[i-1]);
			}
			arr[x] = temp;
			return ans;
		}
		public int getParent(int x) {
			while (parent[x] != x) {
				parent[x] = parent[parent[x]];
				x = parent[x];
			}
			return x;
		}
		void getFactors(int n,int x){
			for(int i = 1;i*i<=n;i++){
				if(n%i==0){
					hs[x].add(i);
					hs[x].add(n/i);
				}
			}
		}
		void recur(int a, int b, int k){
			if(k==0){
				if(a==x2 && b==y2) ans++;
				return;
			}
			recur(a,b+1,k-1);
			recur(a,b-1,k-1);
			recur(a+1,b,k-1);
			recur(a-1,b,k-1);
		}
		int min(int a, int b)
		{
			return (a<b)?a:b;
		}
		
	
		class Pair implements Comparable<Pair>
		{
			int u, v, i;
			Pair(int u, int v) 
			{
				this.u = u;
				this.v = v;
			}
			Pair(int u, int v, int i) 
			{
				this.u = u;
				this.v = v;
				this.i = i;
			}
			public int hashCode()
			{
				return Objects.hash();
			}
			public boolean equals(Object o)
			{
				Pair other = (Pair) o;
				return ((u == other.u && v == other.v));
			}
			public int compareTo(Pair other)
			{
				// return Integer.compare(val, other.val);
				return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)): (Long.compare(v, other.v));//((Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)): (Long.compare(v, other.v)))
						//&(Long.compare(u, other.v) != 0 ? (Long.compare(u, other.v)): (Long.compare(v, other.u))));
			}
			public String toString()
			{
				return this.u + " " + this.v;
			}
		}
	
		int max(int a, int b) 
		{
			if (a > b)
				return a;
			return b;
		}
	
		public static class FenwickTree 
		{
	
			int[] array; // 1-indexed array, In this array We save cumulative
							// information to perform efficient range queries and
							// updates
	
			public FenwickTree(int size) 
			{
				array = new int[size + 1];
			}
	
			public int rsq(int ind)
			{
				assert ind > 0;
				int sum = 0;
				while (ind > 0)
				{
					sum += array[ind];
					// Extracting the portion up to the first significant one of the
					// binary representation of 'ind' and decrementing ind by that
					// number
					ind -= ind & (-ind);
				}
				return sum;
			}
	
			public int rsq(int a, int b) 
			{
				assert b >= a && a > 0 && b > 0;
				return rsq(b) - rsq(a - 1);
			}
	
			public void update(int ind, int value)
			{
				assert ind > 0;
				while (ind < array.length) 
				{
					array[ind] += value;
					// Extracting the portion up to the first significant one of the
					// binary representation of 'ind' and incrementing ind by that
					// number
					ind += ind & (-ind);
				}
			}
	
			public int size() 
			{
				return array.length - 1;
			}
		}
	
		void buildGraph(int n) 
		{
			for (int i = 0; i < n; i++) 
			{
				int x1 = ni(), y1 = ni(), z = ni();
				pmp[x1].add(new Pair(y1,z));
			}
		}
	
		long modInverse(long a, long mOD2) 
		{
			return power(a, mOD2 - 2, mOD2);
		}
	
		long power(long x, long y, long m) 
		{
			if (y == 0)
				return 1;
			long p = power(x, y / 2, m) % m;
			p = (p * p) % m;
	
			return (y % 2 == 0) ? p : (x * p) % m;
		}
	
		public long gcd(long a, long b) 
		{
			if (b == 0)
				return a;
			return gcd(b, a % b);
		}
	
		
	
		static class ST 
		{
			int arr[], lazy[], n;
	
			ST(int a) 
			{
				n = a;
				arr = new int[10 * n];
				lazy = new int[10 * n];
			}
	
			void up(int l, int r, int val)
			{
				update(0, n - 1, 0, l, r, val);
			}
	
			void update(int l, int r, int c, int x, int y, int val)
			{
				if (lazy[c] != 0) {
					lazy[2 * c + 1] += lazy[c];
					lazy[2 * c + 2] += lazy[c];
					if (l == r)
						arr[c] += lazy[c];
					lazy[c] = 0;
				}
				if (l > r || x > y || l > y || x > r)
					return;
				if (x <= l && y >= r) 
				
				{
					lazy[c] += val;
					return;
				}
				int mid = l + r >> 1;
				update(l, mid, 2 * c + 1, x, y, val);
				update(mid + 1, r, 2 * c + 2, x, y, val);
				arr[c] = Math.max(arr[2 * c + 1], arr[2 * c + 2]);
			}
	
			int an(int ind) 
			{
				return ans(0, n - 1, 0, ind);
			}
	
			int ans(int l, int r, int c, int ind) 
			{
				if (lazy[c] != 0) 
				{
					lazy[2 * c + 1] += lazy[c];
					lazy[2 * c + 2] += lazy[c];
					if (l == r)
						arr[c] += lazy[c];
					lazy[c] = 0;
				}
				if (l == r)
					return arr[c];
				int mid = l + r >> 1;
				if (mid >= ind)
					return ans(l, mid, 2 * c + 1, ind);
				return ans(mid + 1, r, 2 * c + 2, ind);
			}
		}
	
		public static int[] shuffle(int[] a, Random gen)
		{
			for (int i = 0, n = a.length; i < n; i++)
			{
				int ind = gen.nextInt(n - i) + i;
				int d = a[i];
				a[i] = a[ind];
				a[ind] = d;
			}
			return a;
		}
	
		long power(long x, long y, int mod) 
		{
			long ans = 1;
			while (y > 0) 
			{
				if (y % 2 == 0) 
				{
					x = (x * x) % mod;
					y /= 2;
				} else 
				{
					ans = (x * ans) % mod;
					y--;
				}
			}
			return ans;
		}
	
		// To Get Input
		// Some Buffer Methods
		private byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;
	
		private int readByte()
		{
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) 
			{
				ptrbuf = 0;
				try 
				{
					lenbuf = is.read(inbuf);
				} catch (IOException e)
				{
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}
	
		private boolean isSpaceChar(int c) 
		{
			return !(c >= 33 && c <= 126);
		}
	
		private int skip() 
		{
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}
	
		private double nd() 
		{
			return Double.parseDouble(ns());
		}
	
		private char nc() 
		{
			return (char) skip();
		}
	
		private String ns()
		{
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b)))
			{ // when nextLine, (isSpaceChar(b) && b != '
										// ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
	
		private char[] ns(int n) 
		{
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b)))
			{
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}
	
		private char[][] nm(int n, int m)
		{
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = ns(m);
			return map;
		}
	
		private int[] na(int n)
		{
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}
	
		private int ni() 
		{
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-')
			{
				minus = true;
				b = readByte();
			}
	
			while (true) 
			{
				if (b >= '0' && b <= '9') 
				{
					num = num * 10 + (b - '0');
				} else 
				{
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	
		private long nl() 
		{
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') 
			{
				minus = true;
				b = readByte();
			}
	
			while (true) 
			{
				if (b >= '0' && b <= '9') 
				{
					num = num * 10 + (b - '0');
				} else 
				{
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	
		private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	
		private void tr(Object... o) 
		{
			if (!oj)
				System.out.println(Arrays.deepToString(o));
		}
	}