#include <cstdio>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <climits>
#include <ctime>
#include <queue>
#include <stack>
#include <algorithm>
#include <list>
#include <vector>
#include <set>
#include <map>
#include <iostream>
#include <deque>
#include <complex>
#include <string>
#include <iomanip>
#include <sstream>
#include <bitset>
#include <valarray>
#include <iterator>
using namespace std;
typedef long long int ll;
typedef unsigned int uint;
typedef unsigned char uchar;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef vector<ll> vi;

#define REP(i,x) for(int i=0;i<(int)(x);i++)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();i++)
#define RREP(i,x) for(int i=((int)(x)-1);i>=0;i--)
#define RFOR(i,c) for(__typeof((c).rbegin())i=(c).rbegin();i!=(c).rend();i++)
#define ALL(container) container.begin(), container.end()
#define RALL(container) container.rbegin(), container.rend()
#define SZ(container) ((int)container.size())
#define mp(a,b) make_pair(a, b)
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );

template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
template<class T> ostream& operator<<(ostream &os, const vector<T> &t) {
os<<"["; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"]"; return os;
}
template<class T> ostream& operator<<(ostream &os, const set<T> &t) {
os<<"{"; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"}"; return os;
}
template<class S, class T> ostream& operator<<(ostream &os, const pair<S,T> &t) { return os<<"("<<t.first<<","<<t.second<<")";}

const ll INF = 1LL<<60;
const double EPS = 1e-8;
const int MOD = 1000000007;


int n;

struct plp{
	ll sum;
	int c;
	int p;
	bool operator< (const plp &opp) const{
		return sum < opp.sum;
	}
	plp(){}
	plp(ll s, int a, int b):sum(s),c(a),p(b){}
};

int main(){
	scanf("%d", &n);
	vi A(n+1);
	vector< set<plp> > vs(n+1);
	REP(i, n) scanf("%lld", &A[i+1]);
	vs[0].insert(plp(-INF, 0, 0));
	REP(i, n+1){
		ll sum = 0;
		for(int j=i+1;j<=n;j++){
			sum += A[j];
			auto it = vs[i].lower_bound(plp(sum, 0, 0));
			if(it == vs[i].begin()) continue;
			-- it;
			int c = it->c + 1;
			auto jt = vs[j].upper_bound(plp(sum, 0, 0));
			if(jt != vs[j].begin()){
				-- jt;
				if(jt->c >= c) continue;
				++ jt;
			}
			while(jt != vs[j].end() && jt->c <= c) jt = vs[j].erase(jt);
			vs[j].insert(plp(sum, c, i));
		}
	}
	auto it = vs[n].end();
	--it;
	int m = it->c;
	printf("%d\n", m);
	vi ans;
	RREP(i, m-1){
		ans.push_back(it->p);
		it = vs[it->p].lower_bound(plp(it->sum, 0, 0));
		-- it;
	}
	RREP(i, ans.size()) printf("%d%s", ans[i], i?" ":"");
	puts("");
	
	
	return 0;
}
### Prompt

Create a solution in cpp for the following problem:

Time passed and Taro became a high school student. Under the influence of my older brother who was a college student, I began to be interested in computer science. Taro read through computer science textbooks and learned that there was a famous problem called the "longest increase subsequence problem." Taro understood this problem, but was wondering if he could create a similar problem himself. Therefore, Taro created the following problem as a result of trial and error.

* There is a sequence A consisting of n integers
* Decompose the sequence A into m sequences with m-1 delimiters. In addition, each sequence after decomposition must always include one or more numbers.
* If the m numbers created by adding all the integers in each of these m sequences are arranged in the order of the original sequence, it becomes a strict increasing sequence (that is, the resulting sequence is Bi <Bi + 1). I want to do it.
* The goal is to maximize the length m of the final sequence B.



For example, consider the case where the sequence A is {5, -4,10, -3,8}.
Prepare a sequence C that represents the position of the delimiter, and set C = {2,4}.
At this time, the sequence A is divided into the parts (5, -4), (10, -3), (8), and when these interiors are added together, they become 1,7,8, respectively, and the resulting sequence B is {1, 7,8}.

<image>

Taro named this problem the "longest increase subsequence problem" and also considered an algorithm to solve it.
And I contacted you as a member of society to check it. Your job is to create a program to solve the problems created by Taro who has grown up.
Since it is my job to check, it also outputs the position of the m-1 delimiter. In addition, there may be multiple such delimiters for the optimum m, but if this m is output correctly, one of the possible ones should be output.

Constraints

> 1 ≤ n ≤ 4000
> | Ai | ≤ 108
>

* For the integer k, | k | represents the absolute value of k

Input

N + 1 integers are given, separated by line breaks.

> n
> A1
> A2
> ...
> An
>

* n represents the length of the given sequence A
* Ai represents the i-th element of the sequence A.

Output

> m
> C1 C2 .. Cm-1
>

* The first line outputs one integer m. m represents the length of the final sequence B. The second line outputs m-1 integer Ci separated by blanks. Ci represents the i-th delimiter when the sequence A is appropriately divided into m parts. See the figure for the definition of the delimiter. Note that 1 ≤ Ci <n is satisfied. The m-1 integer sequence C in the second row must be arranged in ascending order. Therefore, if i <j, then Ci <Cj holds.


* If m = 1, the second line will be blank.
* When the sequence B is generated from the sequence A according to the sequence C, when the sequence B is not an increasing sequence (that is, when i (1 ≤ i <m) such that Bi ≥ Bi + 1 exists), it becomes WrongAnswer.

Examples

Input

3
1
2
4


Output

3
1 2


Input

3
2
2
2


Output

2
1


Input

3
4
2
1


Output

1
(空行)

### Response

```cpp
#include <cstdio>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <climits>
#include <ctime>
#include <queue>
#include <stack>
#include <algorithm>
#include <list>
#include <vector>
#include <set>
#include <map>
#include <iostream>
#include <deque>
#include <complex>
#include <string>
#include <iomanip>
#include <sstream>
#include <bitset>
#include <valarray>
#include <iterator>
using namespace std;
typedef long long int ll;
typedef unsigned int uint;
typedef unsigned char uchar;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef vector<ll> vi;

#define REP(i,x) for(int i=0;i<(int)(x);i++)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();i++)
#define RREP(i,x) for(int i=((int)(x)-1);i>=0;i--)
#define RFOR(i,c) for(__typeof((c).rbegin())i=(c).rbegin();i!=(c).rend();i++)
#define ALL(container) container.begin(), container.end()
#define RALL(container) container.rbegin(), container.rend()
#define SZ(container) ((int)container.size())
#define mp(a,b) make_pair(a, b)
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );

template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
template<class T> ostream& operator<<(ostream &os, const vector<T> &t) {
os<<"["; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"]"; return os;
}
template<class T> ostream& operator<<(ostream &os, const set<T> &t) {
os<<"{"; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"}"; return os;
}
template<class S, class T> ostream& operator<<(ostream &os, const pair<S,T> &t) { return os<<"("<<t.first<<","<<t.second<<")";}

const ll INF = 1LL<<60;
const double EPS = 1e-8;
const int MOD = 1000000007;


int n;

struct plp{
	ll sum;
	int c;
	int p;
	bool operator< (const plp &opp) const{
		return sum < opp.sum;
	}
	plp(){}
	plp(ll s, int a, int b):sum(s),c(a),p(b){}
};

int main(){
	scanf("%d", &n);
	vi A(n+1);
	vector< set<plp> > vs(n+1);
	REP(i, n) scanf("%lld", &A[i+1]);
	vs[0].insert(plp(-INF, 0, 0));
	REP(i, n+1){
		ll sum = 0;
		for(int j=i+1;j<=n;j++){
			sum += A[j];
			auto it = vs[i].lower_bound(plp(sum, 0, 0));
			if(it == vs[i].begin()) continue;
			-- it;
			int c = it->c + 1;
			auto jt = vs[j].upper_bound(plp(sum, 0, 0));
			if(jt != vs[j].begin()){
				-- jt;
				if(jt->c >= c) continue;
				++ jt;
			}
			while(jt != vs[j].end() && jt->c <= c) jt = vs[j].erase(jt);
			vs[j].insert(plp(sum, c, i));
		}
	}
	auto it = vs[n].end();
	--it;
	int m = it->c;
	printf("%d\n", m);
	vi ans;
	RREP(i, m-1){
		ans.push_back(it->p);
		it = vs[it->p].lower_bound(plp(it->sum, 0, 0));
		-- it;
	}
	RREP(i, ans.size()) printf("%d%s", ans[i], i?" ":"");
	puts("");
	
	
	return 0;
}
```