Problem: 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.

Examples

Input

3


Output

Yes
1 2
2 3
3 4
4 5
5 6


Input

1


Output

No

Solution (in CPP):

Solution:
#include <cstdio>

int N;

int main() {
	scanf("%d", &N);
	if (N == (N & -N)) return puts("No"), 0;
	puts("Yes");
	int M = 1 << (31 - __builtin_clz(N));
	printf("%d 1\n", M);
	printf("1 %d\n", M + 1);
	printf("%d %d\n", M + 1, M + N);
	printf("%d %d\n", M + N, 1 + N);
	printf("%d %d\n", 1 + N, M + 1 + N);
	for (int i = 2; i < N; i += 2) if (i != M)
		printf("%d %d\n", i + 1 + N, i),
		printf("%d 1\n", i),
		printf("1 %d\n", i + 1),
		printf("%d %d\n", i + 1, i + N);
	if (~N & 1)
		printf("%d %d\n", N, M + 1),
		printf("%d %d\n", N - M, N + N);
	return 0;
}