Problem:
Score : 700 points

Problem Statement

You are given an integer N. Determine if there exists a tree with 2N vertices numbered 1 to 2N satisfying the following condition, and show one such tree if the answer is yes.

Assume that, for each integer i between 1 and N (inclusive), Vertex i and N+i have the weight i. Then, for each integer i between 1 and N, the bitwise XOR of the weights of the vertices on the path between Vertex i and N+i (including themselves) is i.

Constraints

N is an integer.

1 \leq N \leq 10^{5}

Input

Input is given from Standard Input in the following format:

N

Output

If there exists a tree satisfying the condition in the statement, print Yes; otherwise, print No.
Then, if such a tree exists, print the 2N-1 edges of such a tree in the subsequent 2N-1 lines, in the following format:

a_{1} b_{1}
\vdots
a_{2N-1} b_{2N-1}

Here each pair (a_i, b_i) means that there is an edge connecting Vertex a_i and b_i. The edges may be printed in any order.

Sample Input 1

3

Sample Output 1

Yes
1 2
2 3
3 4
4 5
5 6

The sample output represents the following graph:

Sample Input 2

1

Sample Output 2

No

There is no tree satisfying the condition.

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
)

func main() {
	var n int
	fmt.Scan(&n)
	if n == 1 {
		fmt.Println("No")
	} else {
		switch n % 4 {
		case 0, 2:
			fmt.Println("No")
		case 1:
			fmt.Println("Yes")
			p(2, 3)
			p(3, 1)
			p(1, n+2)
			p(n+2, n+3)

			p(1, 4)
			for i := 4; i < n; i++ {
				p(i, i+1)
			}

			p(n, n+1)
			p(n+1, n+4)
			for i := n + 4; i < 2*n; i++ {
				p(i, i+1)
			}

		case 3:
			fmt.Println("Yes")
			for i := 0; i < n*2-1; i++ {
				p(i+1, i+2)
			}
		}
	}
}

func p(a, b int) {
	fmt.Printf("%d %d\n", a, b)
}