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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"bytes"
	"fmt"
	"io"
	"os"
	"sort"
	"strconv"
)

var DEBUG = true

// -----------------------------------------------------------------------------

// IO helper functions

// Returns next token from input.  It must be initialized by SetInput()
// before the first call.
var nextToken func() ([]byte, error)
var nextLine func() ([]byte, error)

// Holds a buffer for output.  It must be initialized by SetOutput().
// All IO functions (read*() and [e]print*()) should write to OutputWriter
// instead of this.
var OutputBuffer *bufio.Writer

// Holds an io.Writer.  It must be initialized by SetOutput()
var OutputWriter io.Writer

// Set IO functions for interactive input/output.
func SetInteractive(w io.Writer, r io.Reader) {
	SetUnbufferedInput(r)
	OutputBuffer = nil
	OutputWriter = w
}

// Setup OutputBuffer and OutputWriter.
func SetOutput(w io.Writer) {
	OutputBuffer = bufio.NewWriter(w)
	OutputWriter = OutputBuffer
}

// Flushes OutputBuffer
func Flush() {
	if OutputBuffer != nil {
		OutputBuffer.Flush()
	}
}

// Returns true if c is a white space
func IsSpace(c byte) bool {
	switch c {
	case '\t', '\n', '\v', '\f', '\r', ' ':
		return true
	}
	return false
}

func IsNewLine(c byte) bool {
	switch c {
	case '\n', '\r':
		return true
	}
	return false
}

// Setup nextToken with input buffer.
func SetInput(r io.Reader) {
	buf := new(bytes.Buffer)
	var b []byte

	var i int
	rest := func() ([]byte, error) {
		for i < len(b) && IsSpace(b[i]) {
			i++
		}
		if i == len(b) {
			return nil, io.ErrUnexpectedEOF
		}
		j := i
		for i < len(b) && !IsSpace(b[i]) {
			i++
		}
		return b[j:i], nil
	}
	initial := func() ([]byte, error) {
		io.Copy(buf, r)
		b = buf.Bytes()
		nextToken = rest
		return rest()
	}
	nextToken = initial

	restLn := func() ([]byte, error) {
		for i < len(b) && IsNewLine(b[i]) {
			i++
		}
		if i == len(b) {
			return nil, io.ErrUnexpectedEOF
		}
		j := i
		for i < len(b) && !IsNewLine(b[i]) {
			i++
		}
		return b[j:i], nil
	}

	initialLn := func() ([]byte, error) {
		io.Copy(buf, r)
		b = buf.Bytes()
		nextLine = restLn
		return restLn()
	}
	nextLine = initialLn
}

// Setup nextToken without input buffer.
func SetUnbufferedInput(r io.Reader) {
	buf := bufio.NewReader(r)
	var b []byte

	var i int
	nextToken = func() ([]byte, error) {
		var err error
		if i == len(b) {
			b, err = buf.ReadBytes('\n')
			if err != nil {
				return nil, err
			}
			i = 0
			j := len(b) - 1
			for 0 <= j && IsSpace(b[j]) {
				j--
			}
			b = b[0 : j+1]
		}
		for i < len(b) && IsSpace(b[i]) {
			i++
		}
		j := i
		for i < len(b) && !IsSpace(b[i]) {
			i++
		}
		if i == j {
			return nil, io.ErrUnexpectedEOF
		}
		return b[j:i], nil
	}
}

// -----------------------------------------------------------------------------

// IO functions

// Reads next token and return it as []byte
func readb() []byte {
	b, err := nextToken()
	if err != nil {
		panic(err)
	}
	return b[:len(b):len(b)]
}

// Reads next token and return it as string
func reads() string {
	return string(readb())
}

// Read next line as []byte.  Trailing '\n' will not be included.
// See also comments on readb()
func readbln() []byte {
	b, err := nextLine()
	if err != nil {
		panic(err)
	}
	return b[:len(b):len(b)]
}

// Read next line as string
func readsln() string {
	return string(readbln())
}

// Reads next token and return it as int64
func readll() int64 {
	i, err := strconv.ParseInt(reads(), 10, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

// Reads next token and return it as int
func readi() int {
	return int(readll())
}

// Reads next token and return it as float64
func readf() float64 {
	f, err := strconv.ParseFloat(reads(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

// Write args to OutputWriter with the format f
func printf(f string, args ...interface{}) (int, error) {
	return fmt.Fprintf(OutputWriter, f, args...)
}

// Write args to OutputWriter without format
func println(args ...interface{}) (int, error) {
	return fmt.Fprintln(OutputWriter, args...)
}

// Write args to stderr with the format f
func eprintf(f string, args ...interface{}) (int, error) {
	return fmt.Fprintf(os.Stderr, f, args...)
}

// Write args to stderr without format
func eprintln(args ...interface{}) (int, error) {
	return fmt.Fprintln(os.Stderr, args...)
}

func debugf(f string, args ...interface{}) {
	if !DEBUG {
		return
	}
	fmt.Fprintf(os.Stderr, f, args...)
}

func debug(args ...interface{}) {
	if !DEBUG {
		return
	}
	fmt.Fprintln(os.Stderr, args...)
}

// -----------------------------------------------------------------------------

// Utilities

func sumSlice(a []int) int {
	var res int
	for _, v := range a {
		res += v
	}
	return res
}

func sumSlicell(a []int64) int64 {
	var res int64
	for _, v := range a {
		res += v
	}
	return res
}

func readInts(N int) (int, []int) {
	if N == 0 {
		N = readi()
	}
	a := make([]int, N)
	for i := range a {
		a[i] = readi()
	}
	return N, a
}

func readIntsll(N int) (int, []int64) {
	if N == 0 {
		N = readi()
	}
	a := make([]int64, N)
	for i := range a {
		a[i] = readll()
	}
	return N, a
}

// -----------------------------------------------------------------------------

// Simple math functions

const (
	// big prime
	INF  = 1000000007
	INF2 = 1000000009
	INF3 = 998244353
)

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func minll(a, b int64) int64 {
	if a < b {
		return a
	}
	return b
}

func minf(a, b float64) float64 {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a < b {
		return b
	}
	return a
}

func maxll(a, b int64) int64 {
	if a < b {
		return b
	}
	return a
}

func maxf(a, b float64) float64 {
	if a < b {
		return b
	}
	return a
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

func absll(a int64) int64 {
	if a < 0 {
		return -a
	}
	return a
}

func absf(a float64) float64 {
	if a < 0 {
		return -a
	}
	return a
}

// egcd(a, b) returns d, x, y:
//   d is gcd(a,b)
//   x, y are  integers that satisfy ax + by = d
func egcd(a, b int) (int, int, int) {
	if b == 0 {
		return a, 1, 0
	}
	d, x, y := egcd(b, a%b)
	return d, y, x - a/b*y
}

func egcdll(a, b int64) (int64, int64, int64) {
	if b == 0 {
		return a, 1, 0
	}
	d, x, y := egcdll(b, a%b)
	return d, y, x - a/b*y
}

func gcd(a, b int) int {
	d, _, _ := egcd(a, b)
	return d
}

func gcdll(a, b int64) int64 {
	d, _, _ := egcdll(a, b)
	return d
}

// set up IO functions
func init() {
	// for non-interactive
	SetInput(os.Stdin)
	SetOutput(os.Stdout)

	// Enable below when interactive.  Its ok to leave above intact.
	SetInteractive(os.Stdout, os.Stdin)
}

func main() {
	defer Flush()
	n := readi()
	t := make([]task, n)
	maxB := 0
	for i := 0; i < n; i++ {
		t[i] = task{readi(), readi()}
		maxB = max(maxB, t[i].b)
	}

	answer := solve(n, t, maxB)
	if answer <= 0 {
		println("Yes")
	} else {
		println("No")
	}
}

type task struct {
	a, b int
}

type ByEnd []task

func (a ByEnd) Len() int           { return len(a) }
func (a ByEnd) Less(i, j int) bool { return a[i].b < a[j].b }
func (a ByEnd) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }

func solve(n int, t []task, maxB int) int {
	DEBUG = false
	sort.Sort(ByEnd(t))
	pile := 0
	tIndex := len(t) - 1
	for i := maxB; i > 0; i-- {
		for tIndex >= 0 && t[tIndex].b == i {
			pile += t[tIndex].a
			tIndex--
		}

		if pile > 0 {
			pile--
		}
	}
	// debug(pile)
	return pile
}