CODE FESTIVAL 2016 Relay (Parallel) - Connected Checkerboard

We have an N×N checkerboard.

From the square at the upper left corner, a square that is i squares to the right and j squares below is denoted as (i, j). Particularly, the square at the upper left corner is denoted as (0, 0).

Each square (i, j) such that i+j is even, is colored black, and the other squares are colored white.

We will satisfy the following condition by painting some of the white squares:

* Any black square can be reached from square (0, 0) by repeatedly moving to a black square that shares a side with the current square.



Achieve the objective by painting at most 170000 squares black.

Constraints

* 1 \leq N \leq 1,000

Input

The input is given from Standard Input in the following format:


N


Output

Print the squares to paint in the following format:


K
x_1 y_1
x_2 y_2
:
x_K y_K


This means that a total of K squares are painted black, the i-th of which is (x_i, y_i).

Judging

The output is considered correct only if all of the following conditions are satisfied:

* 0 \leq K \leq 170000
* 0 \leq x_i, y_i \leq N-1
* For each i, x_i + y_i is odd.
* If i \neq j, then (x_i, y_i) \neq (x_j, y_j).
* The condition in the statement is satisfied by painting all specified squares.

Examples

Input

2


Output

1
1 0


Input

4


Output

3
0 1
2 1
2 3

Source: atcoder | Difficulty: UNKNOWN_DIFFICULTY


Solutions:
n = int(input())
ans = []
for i in range(n - 1):
	if i % 2:
		ans += [(i, 0)]
for i in range(n - 1):
	if i % 6 == 1:
		for j in range(2, n):
			if j % 2 == 0:
				ans += [(i, j)]
	if i % 6 == 4:
		for j in range(n):
			if j % 2:
				ans += [(i, j)]
for j in range(n):
	if (n - 1 + j) % 2:
		ans += [(n - 1, j)]
print(len(ans))
for (x, y) in ans:
	print(x, y)


N = int(input())
MAX = 170000
ans = []
for i in range(1, N, 2):
	for j in range(0, N, 2):
		if i // 2 % 3 == 0:
			ans.append((i, j))
		elif i // 2 % 3 == 1:
			if j // 2 % 2 == 0:
				ans.append((i, j))
		elif j // 2 % 2 == 1:
			ans.append((i, j))
for i in [0, N - 1]:
	for j in range(N):
		if (i + j) % 2:
			ans.append((i, j))
			ans.append((j, i))
ans = set(ans)
print(len(ans))
for (x, y) in ans:
	print('{0} {1}'.format(x, y))


n = int(input())
ans_list = []
for i in range(n):
	if i % 2 == 1:
		ans_list.append((i, 0))
	if i % 6 == 1:
		for j in range(2, n, 2):
			ans_list.append((i, j))
	elif i % 6 == 4:
		for j in range(1, n, 2):
			ans_list.append((i, j))
if n % 3 != 2:
	for i in range(1, n):
		if (n - 1 + i) % 2 == 1:
			ans_list.append((n - 1, i))
print(len(ans_list))
for i in ans_list:
	print(*i)


n = int(input())
odd = [item for item in range(3, n + 1, 2)]
even = [item for item in range(2, n + 1, 2)]
ans = []
added = [0] * n
for i in range(2, n + 1, 2):
	ans.append((1, i))
for i in range(2, n + 1, 3):
	if i % 2 == 0:
		for item in odd:
			ans.append((item, i))
	else:
		for item in even:
			ans.append((item, i))
for i in range(n, 0, -1):
	if (i - 2) % 3 == 0:
		continue
	if i % 2 == 0:
		for item in odd:
			ans.append((item, i))
		break
ans.sort()
print(len(ans))
for (a, b) in ans:
	print(a - 1, b - 1)