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 C# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;

namespace D
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[,] AB = new int[n,2];
            int bmax = 0;
            for(int i = 0; i < n; i++)
            {
                string[] In = Console.ReadLine().Split(' ');
                int a = int.Parse(In[0]);
                int b = int.Parse(In[1]);
                b--;
                if (b > bmax) bmax = b;
                AB[i, 0] =a;
                AB[i, 1] =b;
            }
            var L = new List<int>[bmax+1];
            for(int i = 0; i < bmax + 1; i++)
            {
                L[i] = new List<int>();
            }
            for(int i = 0; i < n; i++)
            {
                L[AB[i, 1]].Add(AB[i, 0]);
            }
            var T = new PriorityQueue<int>(n);
            bool flag = true;
            for(int i = bmax; i >= 0; i--)
            {
                if (L[i].Count == 0 && T.Count==0) continue;
                if (L[i].Count != 0) { foreach (var l in L[i]) T.Push(l); }
                if (T.Count != 0) i -= (T.Pop()-1);
                if (i < 0) { flag = false; break; }
            }
            if (T.Count == 0 && flag) Console.WriteLine("Yes");
            else Console.WriteLine("No");
        }
    }

    class PriorityQueue<T> where T : IComparable<T>
    {
        private readonly T[] _array;
        private readonly IComparer _comparer;
        public int Count { get; private set; } = 0;
        public T Root => _array[0];

        public PriorityQueue(int capacity, IComparer comparer = null)
        {
            _array = new T[capacity];
            _comparer = comparer;
        }

        /// <summary>
        /// 要素を挿入する
        /// </summary>
        public void Push(T item)
        {
            _array[this.Count] = item;
            Count += 1;

            var n = Count - 1;                  // 末尾(追加した)のノードの番号
            while (n != 0)
            {
                var parent = (n - 1) / 2;       // 親ノードの番号

                if (Compare(_array[n], _array[parent]) > 0)
                {
                    Swap(n, parent);
                    n = parent;
                }
                else
                {
                    break;
                }
            }
        }

        /// <summary>
        /// 優先度の一番高いものを取り出す
        /// </summary>
        public T Pop()
        {
            Swap(0, this.Count - 1);            // 先頭要素を末尾にする
            Count -= 1;

            var parent = 0;                     // 親ノードの番号
            while (true)
            {
                var child = 2 * parent + 1;     // 子ノードの番号
                if (child > Count - 1) break;

                // 値の大きい方の子を選ぶ
                if (child < Count - 1 && Compare(_array[child], _array[child + 1]) < 0) child += 1;

                // 子の方が親より大きければ入れ替える
                if (Compare(_array[parent], _array[child]) < 0)
                {
                    Swap(parent, child);
                    parent = child;
                }
                else
                {
                    break;
                }
            }

            return _array[Count];
        }

        /// <summary>
        /// 大きいものから列挙していく
        /// withPop = falseのときは順番関係なく取り出しもしないが素早く全要素を取得できる　
        /// </summary>
        public IEnumerable<T> GetAllElements(bool withPop = true)
        {
            int count = Count;
            for (int i = 0; i < count; i++)
            {
                if (withPop) yield return Pop();
                else yield return _array[count - i - 1];
            }
        }

        private int Compare(T a, T b)
        {
            if (_comparer == null) return a.CompareTo(b);
            return _comparer.Compare(a, b);
        }

        private void Swap(int a, int b)
        {
            var tmp = _array[a];
            _array[a] = _array[b];
            _array[b] = tmp;
        }
    }
}