Problem:
Score: 400 points

Problem Statement

Kizahashi, who was appointed as the administrator of ABC at National Problem Workshop in the Kingdom of AtCoder, got too excited and took on too many jobs.

Let the current time be time 0. Kizahashi has N jobs numbered 1 to N.

It takes A_i units of time for Kizahashi to complete Job i. The deadline for Job i is time B_i, and he must complete the job before or at this time.

Kizahashi cannot work on two or more jobs simultaneously, but when he completes a job, he can start working on another immediately.

Can Kizahashi complete all the jobs in time? If he can, print Yes; if he cannot, print No.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

1 \leq A_i, B_i \leq 10^9 (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N
A_1 B_1
.
.
.
A_N B_N

Output

If Kizahashi can complete all the jobs in time, print Yes; if he cannot, print No.

Sample Input 1

5
2 4
1 9
1 8
4 9
3 12

Sample Output 1

Yes

He can complete all the jobs in time by, for example, doing them in the following order:

Do Job 2 from time 0 to 1.

Do Job 1 from time 1 to 3.

Do Job 4 from time 3 to 7.

Do Job 3 from time 7 to 8.

Do Job 5 from time 8 to 11.

Note that it is fine to complete Job 3 exactly at the deadline, time 8.

Sample Input 2

3
334 1000
334 1000
334 1000

Sample Output 2

No

He cannot complete all the jobs in time, no matter what order he does them in.

Sample Input 3

30
384 8895
1725 9791
170 1024
4 11105
2 6
578 1815
702 3352
143 5141
1420 6980
24 1602
849 999
76 7586
85 5570
444 4991
719 11090
470 10708
1137 4547
455 9003
110 9901
15 8578
368 3692
104 1286
3 4
366 12143
7 6649
610 2374
152 7324
4 7042
292 11386
334 5720

Sample Output 3

Yes

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.function.Supplier;

public class Main {

    static void solve() {
        int n = nextInt();

        List<Task> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            long a = nextLong();
            int b = nextInt();
            list.add(new Task(a, b));
        }
        sort(list);

        boolean ok = true;
        long sum = 0;
        for (int i = 0; i < n; i++) {
            Task task = list.get(i);
            sum += task.a;
            if (sum > task.b) {
                ok = false;
                break;
            }
        }

        if (ok)
            out.println("Yes");
        else {
            out.println("No");
        }
    }

    static class Task implements Comparable<Task> {
        long a;
        int b;

        Task(long a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(Task o) {
            return b - o.b;
        }
    }

    static final int MOD = 1_000_000_007;
    static long[] fac, finv, inv;

    // 階乗(n!)
    static long factorial(long n) {
        long ans = 1;
        for (long i = n; i > 0; i--) {
            ans = ans * i % MOD;
        }
        return ans;
    }

    // nCkの初期化
    static void comInit(int max) {
        fac = new long[max];
        finv = new long[max];
        inv = new long[max];
        fac[0] = fac[1] = 1;
        finv[0] = finv[1] = 1;
        inv[1] = 1;

        for (int i = 2; i < max; i++) {
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }

    // nCkの計算
    static long com(int n, int k) {
        if (n < k)
            return 0;
        if (n < 0 || k < 0)
            return 0;
        return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
    }

    static Map<Integer, List<Integer>> primeFactors = new HashMap<>();

    // 素因数分解
    static List<Integer> primeFactorize(int n) {
        if (primeFactors.containsKey(n))
            return primeFactors.get(n);

        List<Integer> list = new ArrayList<>();
        if (n % 2 == 0) {
            list.addAll(primeFactorize(n / 2));
            list.add(2);
        } else {
            boolean ok = true;
            for (int j = 3; j * j <= n; j += 2) {
                if (n % j == 0) {
                    list.addAll(primeFactorize(n / j));
                    list.addAll(primeFactorize(j));
                    ok = false;
                    break;
                }
            }
            if (ok) {
                if (n != 1)
                    list.add(n);
            }
        }

        primeFactors.put(n, Collections.unmodifiableList(list));
        return list;
    }

    // 2〜nまでの数値を素因数分解したmapを返す.
    // map: 数値 -> (素因数)
    // ex)
    // 2 -> (2)
    // 4 -> (2,2)
    // 12 -> (2,2,3)
    @Deprecated // primeFactorizeを使うべき
    static Map<Integer, List<Integer>> primeFactorizeTo(int n) {
        Map<Integer, List<Integer>> map = new HashMap<>();
        for (int i = 2; i <= n; i++) {
            List<Integer> list = new ArrayList<>();
            int tmp = i;
            for (int j = i - 1; j > 1; j--) {
                if (tmp % j == 0) {
                    if (map.containsKey(j)) {
                        list.addAll(map.get(j));
                    } else {
                        list.add(j);
                    }
                    tmp /= j;
                }
            }
            if (tmp != 1)
                list.add(tmp);
            map.put(i, list);
        }
        return map;
    }

    static PrintWriter out;
    static Scanner sc;
    static boolean debugEnabled;
    static long start;
    static long end;

    static int[][] newIntArray(int h, int w, int value) {
        int[][] ret = new int[h][w];
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                ret[i][j] = value;
            }
        }
        return ret;
    }

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

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

    static String nextString() {
        return sc.next();
    }

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

    static long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextLong();
        }
        return a;
    }

    static List<Integer> nextIntList(int n) {
        List<Integer> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            list.add(nextInt());
        }
        return list;
    }

    static List<Double> nextDoubleList(int n) {
        List<Double> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            list.add((double) nextInt());
        }
        return list;
    }

    static List<Long> nextLongList(int n) {
        List<Long> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            list.add(nextLong());
        }
        return list;
    }

    static char[][] nextCharArray(int h, int w) {
        char[][] c = new char[h][w];
        for (int i = 0; i < h; i++) {
            String str = nextString();
            for (int j = 0; j < w; j++) {
                c[i][j] = str.charAt(j);
            }
        }
        return c;
    }

    // 昇順
    static <T extends Comparable<? super T>> List<T> sort(List<T> list) {
        return sortAsc(list);
    }

    // 昇順
    static <T extends Comparable<? super T>> List<T> sortAsc(List<T> list) {
        Collections.sort(list);
        return list;
    }

    // 降順
    static <T extends Comparable<? super T>> List<T> sortDesc(List<T> list) {
        Collections.sort(list, (e1, e2) -> e2.compareTo(e1));
        return list;
    }

    // greatest common divisor
    // 最大公約数
    static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    // least common multiple
    // 最小公倍数
    static long lcm(long a, long b) {
        if (a > b) {
            return (a / gcd(a, b)) * b;
        } else {
            return (b / gcd(a, b)) * a;
        }
    }

    // least common multiple
    // 最小公倍数
    // 素因数分解されたListを引数とした場合
    static List<Integer> lcm(List<Integer> a, List<Integer> b) {
        List<Integer> ret = new ArrayList<>(a);
        List<Integer> tmp = new ArrayList<>(b);
        for (Integer i : a) {
            if (tmp.contains(i))
                tmp.remove(i);
        }
        ret.addAll(tmp);
        return ret;
    }

    // baseのn乗を計算を返す
    static int pow(int base, int n) {
        int ret = 1;
        for (int i = 0; i < n; i++) {
            ret *= base;
        }
        return ret;
    }

    // return n^k mod m
    static long powMod(long n, long k, long m) {
        if (k == 0) {
            return 1;
        } else if (k % 2 == 1) {
            return powMod(n, k - 1, m) * n % m;
        } else {
            long tmp = powMod(n, k / 2, m);
            return tmp * tmp % m;
        }
    }

    // intをlength桁のbit文字列に変換
    static String toBitString(int length, int n) {
        StringBuilder sb = new StringBuilder();
        for (int i = length - 1; i >= 0; i--) {
            if ((n >> i) % 2 == 1) {
                sb.append("1");
            } else {
                sb.append("0");
            }
        }
        return sb.toString();
    }

    static void setDebugEnabled() {
        String className = new Object() {
        }.getClass().getEnclosingClass().getSimpleName();

        if (!className.equals("Main"))
            debugEnabled = true;
    }

    static void debug(String msg) {
        if (debugEnabled)
            System.err.println(msg);
    }

    static void debug(Supplier<String> msg) {
        if (debugEnabled)
            System.err.println(msg.get());
    }

    static class UnionFind {
        int[] parent;

        UnionFind(int n) {
            parent = new int[n];
            init();
        }

        void init() {
            for (int i = 0; i < parent.length; i++) {
                parent[i] = i;
            }
        }

        int getRoot(int i) {
            if (parent[i] == i) {
                return i;
            } else {
                return parent[i] = getRoot(parent[i]);
            }
        }

        boolean isSame(int x, int y) {
            return getRoot(x) == getRoot(y);
        }

        void unit(int x, int y) {
            x = getRoot(x);
            y = getRoot(y);
            if (x != y) {
                parent[x] = y;
            }

        }
    }

    public static void main(String[] args) {
        preProcess();
        // System.exit(0)で終了した場合も、解答を出力するためにはshutdown hookの設定が必要
        // しかし、これを有効化すると100[msec]程度処理時間が長くなる
        // Runtime.getRuntime().addShutdownHook(new Thread(() -> postProcess()));
        solve();
        postProcess();
    }

    static void preProcess() {
        start = System.nanoTime();
        setDebugEnabled();
        out = new PrintWriter(System.out);
        sc = new Scanner(System.in);
    }

    static void postProcess() {
        out.flush();
        sc.close();
        end = System.nanoTime();
        debug(() -> "elapsed time: " + (end - start) / 1_000_000 + "[msec]");
    }

}