Problem:
Score : 700 points

Problem Statement

In the final of CODE FESTIVAL in some year, there are N participants.
The height and power of Participant i is H_i and P_i, respectively.

Ringo is hosting a game of stacking zabuton (cushions).

The participants will line up in a row in some order, and they will in turn try to add zabuton to the stack of zabuton.
Initially, the stack is empty.
When it is Participant i's turn, if there are H_i or less zabuton already stacked, he/she will add exactly P_i zabuton to the stack. Otherwise, he/she will give up and do nothing.

Ringo wants to maximize the number of participants who can add zabuton to the stack.
How many participants can add zabuton to the stack in the optimal order of participants?

Constraints

1 \leq N \leq 5000

0 \leq H_i \leq 10^9

1 \leq P_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
H_1 P_1
H_2 P_2
:
H_N P_N

Output

Print the maximum number of participants who can add zabuton to the stack.

Sample Input 1

3
0 2
1 3
3 4

Sample Output 1

2

When the participants line up in the same order as the input, Participants 1 and 3 will be able to add zabuton.

On the other hand, there is no order such that all three participants can add zabuton. Thus, the answer is 2.

Sample Input 2

3
2 4
3 1
4 1

Sample Output 2

3

When the participants line up in the order 2, 3, 1, all of them will be able to add zabuton.

Sample Input 3

10
1 3
8 4
8 3
9 1
6 4
2 3
4 2
9 2
8 3
0 1

Sample Output 3

5

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <queue>
#include <stack>
#include <algorithm>
#include <cmath>
#include <string>
#include <cstring>
#include <map>
#include <set>
#include <bitset>
#include <sstream>
#include <cstdlib>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <climits>
#include <ctype.h>
using namespace std;

#define PI acos(-1.0)
#define EPS 1e-8
#define MOD 1000000007
#define all(x) (x).begin(), (x).end()
#define pb push_back
#define fi first
#define se second

typedef long double ld;
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;

struct Matrix {
    vvi data;
    int r, c;
    Matrix(int row, int col, bool identity = false) : r(row), c(col) {
        data.assign(row, vector<int>(col, 0));
        if (identity) {
            for (int i = 0; i < r; ++i) {
                data[i][i] = 1;
            }
        }
    }
    Matrix operator * (Matrix& other) {
        int m = r, n = c, p = other.c;
        Matrix res(m, p);
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < p; ++j) {
                for (int k = 0; k < n; ++k) {
                    res.data[i][j] += data[i][k] * other.data[k][j];
                }
            }
        }
        return res;
    }
};

// 扩展欧几里得算法 res[1] * a + res[2] * b = res[0] = gcd(a, b)
vector<int> extendGcd(int a, int b) {
    if (b == 0) {
        return {a, 1, 0};
    } else {
        vector<int> tmp = extendGcd(b, a % b);
        return {tmp[0], tmp[2], tmp[1] - (a / b) * tmp[2]};
    }
}

// 矩阵快速幂
Matrix matrix_power(Matrix base, ll exp) {
    int n = base.r;
    Matrix res(n, n, true);
    while (exp) {
        if (exp & 1) {
            res = res * base;
        }
        base = base * base;
        exp >>= 1;
    }
    return res;
}

// 带模快速幂
template <typename T>
T power_mod(T base, int exp, int mod = MOD) {
    T res = 1;
    while (exp) {
        if (exp & 1) res = res * base % mod;
        base = base * base % mod;
        exp >>= 1;
    }
    return res;
}

// 快速幂
template <typename T>
T power(T base, int exp) {
    T res = 1;
    while (exp) {
        if (exp & 1) res *= base;
        base *= base;
        exp >>= 1;
    }
    return res;
}

// 求逆元
ll inv(ll a) {
    return power_mod(a, MOD - 2);
}

/******************************** template ********************************/
#define N 5050
int n;
vector<pii> foo;

int main() {
    cin >> n;
    int h, p;
    for (int i = 0; i < n; ++i) {
        cin >> h >> p;
        foo.pb({h, p});
    }
    sort(all(foo));

    auto cmp = [](pii& a, pii& b) {
        return a.se < b.se || (a.se == b.se && a.fi < b.fi);
    };
    priority_queue<pii, vector<pii>, decltype(cmp)> pq(cmp);
    int tot = 0;
    bool flag = true;
    while (flag) {
        flag = false;
        vector<pii> bar;
        for (int i = 0; i < foo.size(); ++i) {
            if (tot <= foo[i].fi) {
                tot += foo[i].se;
                pq.push(foo[i]);
                flag = true;
            } else if (pq.top().se > foo[i].se) {
                tot -= pq.top().se - foo[i].se;
                bar.pb(pq.top());
                pq.pop();
                pq.push(foo[i]);
                flag = true;
            }
        }
        foo = bar;
        sort(all(foo));
    }
    cout << pq.size();

    return 0;
}