Problem:
Score : 500 points

Problem Statement

You are given an integer N. Determine if there exists a tuple of subsets of \{1,2,...N\}, (S_1,S_2,...,S_k), that satisfies the following conditions:

Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.

Any two of the sets S_1,S_2,...,S_k have exactly one element in common.

If such a tuple exists, construct one such tuple.

Constraints

1 \leq N \leq 10^5

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If a tuple of subsets of \{1,2,...N\} that satisfies the conditions does not exist, print No.
If such a tuple exists, print Yes first, then print such subsets in the following format:

k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}

where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.

If there are multiple such tuples, any of them will be accepted.

Sample Input 1

3

Sample Output 1

Yes
3
2 1 2
2 3 1
2 2 3

It can be seen that (S_1,S_2,S_3)=(\{1,2\},\{3,1\},\{2,3\}) satisfies the conditions.

Sample Input 2

4

Sample Output 2

No

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"errors"
	"fmt"
	"io"
	"os"
	"strconv"
)

/*********** I/O ***********/

var (
	// ReadString returns a WORD string.
	ReadString func() string
	stdout     *bufio.Writer
)

func init() {
	ReadString = newReadString(os.Stdin)
	stdout = bufio.NewWriter(os.Stdout)
}

func newReadString(ior io.Reader) func() string {
	r := bufio.NewScanner(ior)
	r.Buffer(make([]byte, 1024), int(1e+11))
	// Split sets the split function for the Scanner. The default split function is ScanLines.
	// Split panics if it is called after scanning has started.
	r.Split(bufio.ScanWords)

	return func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
}

// ReadInt returns an integer.
func ReadInt() int {
	return int(readInt64())
}

func readInt64() int64 {
	i, err := strconv.ParseInt(ReadString(), 0, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

// ReadIntSlice returns an integer slice that has n integers.
func ReadIntSlice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt()
	}
	return b
}

// ReadRuneSlice returns a rune slice.
func ReadRuneSlice() []rune {
	return []rune(ReadString())
}

/*********** Debugging ***********/

// ZeroPaddingRuneSlice returns binary expressions of integer n with zero padding.
// For debugging use.
func ZeroPaddingRuneSlice(n, digitsNum int) []rune {
	sn := fmt.Sprintf("%b", n)

	residualLength := digitsNum - len(sn)
	if residualLength <= 0 {
		return []rune(sn)
	}

	zeros := make([]rune, residualLength)
	for i := 0; i < len(zeros); i++ {
		zeros[i] = '0'
	}

	res := []rune{}
	res = append(res, zeros...)
	res = append(res, []rune(sn)...)

	return res
}

/*********** DP sub-functions ***********/

// ChMin accepts a pointer of integer and a target value.
// If target value is SMALLER than the first argument,
//	then the first argument will be updated by the second argument.
func ChMin(updatedValue *int, target int) bool {
	if *updatedValue > target {
		*updatedValue = target
		return true
	}
	return false
}

// ChMax accepts a pointer of integer and a target value.
// If target value is LARGER than the first argument,
//	then the first argument will be updated by the second argument.
func ChMax(updatedValue *int, target int) bool {
	if *updatedValue < target {
		*updatedValue = target
		return true
	}
	return false
}

// NthBit returns nth bit value of an argument.
// n starts from 0.
func NthBit(num, nth int) int {
	return num >> uint(nth) & 1
}

/*********** Arithmetic ***********/

// Max returns the max integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Max(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m < integer {
			m = integer
		}
	}
	return m
}

// Min returns the min integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Min(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m > integer {
			m = integer
		}
	}
	return m
}

// DigitSum returns digit sum of a decimal number.
// DigitSum only accept a positive integer.
func DigitSum(n int) int {
	if n < 0 {
		return -1
	}

	res := 0

	for n > 0 {
		res += n % 10
		n /= 10
	}

	return res
}

// Sum returns multiple integers sum.
func Sum(integers ...int) int {
	s := 0

	for _, i := range integers {
		s += i
	}

	return s
}

// CeilInt returns the minimum integer larger than or equal to float(a/b).
func CeilInt(a, b int) int {
	res := a / b
	if a%b > 0 {
		res++
	}
	return res
}

// FloorInt returns the maximum integer smaller than or equal to float(a/b)
func FloorInt(a, b int) int {
	res := a / b
	return res
}

// PowInt is integer version of math.Pow
// PowInt calculate a power by Binary Power (二分累乗法(O(log e))).
func PowInt(a, e int) int {
	if a < 0 || e < 0 {
		panic(errors.New("[argument error]: PowInt does not accept negative integers"))
	}

	if e == 0 {
		return 1
	}

	if e%2 == 0 {
		halfE := e / 2
		half := PowInt(a, halfE)
		return half * half
	}

	return a * PowInt(a, e-1)
}

// AbsInt is integer version of math.Abs
func AbsInt(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

// Gcd returns the Greatest Common Divisor of two natural numbers.
// Gcd only accepts two natural numbers (a, b >= 1).
// 0 or negative number causes panic.
// Gcd uses the Euclidean Algorithm.
func Gcd(a, b int) int {
	if a <= 0 || b <= 0 {
		panic(errors.New("[argument error]: Gcd only accepts two NATURAL numbers"))
	}
	if a < b {
		a, b = b, a
	}

	// Euclidean Algorithm
	for b > 0 {
		div := a % b
		a, b = b, div
	}

	return a
}

// Lcm returns the Least Common Multiple of two natural numbers.
// Lcd only accepts two natural numbers (a, b >= 1).
// 0 or negative number causes panic.
// Lcd uses the Euclidean Algorithm indirectly.
func Lcm(a, b int) int {
	if a <= 0 || b <= 0 {
		panic(errors.New("[argument error]: Gcd only accepts two NATURAL numbers"))
	}

	// a = a'*gcd, b = b'*gcd, a*b = a'*b'*gcd^2
	// a' and b' are relatively prime numbers
	// gcd consists of prime numbers, that are included in a and b
	gcd := Gcd(a, b)

	// not (a * b / gcd), because of reducing a probability of overflow
	return (a / gcd) * b
}

// Strtoi is a wrapper of `strconv.Atoi()`.
// If `strconv.Atoi()` returns an error, Strtoi calls panic.
func Strtoi(s string) int {
	if i, err := strconv.Atoi(s); err != nil {
		panic(errors.New("[argument error]: Strtoi only accepts integer string"))
	} else {
		return i
	}
}

/********** I/O usage **********/

//str := ReadString()
//i := ReadInt()
//X := ReadIntSlice(n)
//S := ReadRuneSlice()

/*******************************************************************/

const MOD = 1000000000 + 7
const ALPHABET_NUM = 26

var n int

func main() {
	n = ReadInt()

	flag := false
	for m := 1; m*(m+1)/2 <= n; m++ {
		if n == m*(m+1)/2 {
			flag = true
			break
		}
	}

	if !flag {
		fmt.Println("No")
		return
	}

	k := 0
	a := 1 + 8*n
	for i := 1; i*i <= a; i++ {
		if i*i == a {
			k = (1 + i) / 2
			break
		}
	}

	answers := [][]int{}
	for i := 0; i < k; i++ {
		answers = append(answers, []int{})
	}
	num := 1
	for i := 0; i < k-1; i++ {
		for j := i + 1; j < k; j++ {
			answers[i] = append(answers[i], num)
			answers[j] = append(answers[j], num)
			num++
		}
	}

	fmt.Println("Yes")
	fmt.Println(k)
	for i := 0; i < len(answers); i++ {
		row := answers[i]
		fmt.Printf("%d ", len(row))
		for j := 0; j < len(row); j++ {
			if j == len(row)-1 {
				fmt.Printf("%d\n", row[j])
			} else {
				fmt.Printf("%d ", row[j])
			}
		}
	}
}

// MODはとったか？
// 遷移だけじゃなくて最後の最後でちゃんと取れよ？

/*******************************************************************/