Problem:
Score : 700 points

Problem Statement

You are given an integer N.
Build an undirected graph with N vertices with indices 1 to N that satisfies the following two conditions:

The graph is simple and connected.

There exists an integer S such that, for every vertex, the sum of the indices of the vertices adjacent to that vertex is S.

It can be proved that at least one such graph exists under the constraints of this problem.

Constraints

All values in input are integers.

3 \leq N \leq 100

Input

Input is given from Standard Input in the following format:

N

Output

In the first line, print the number of edges, M, in the graph you made. In the i-th of the following M lines, print two integers a_i and b_i, representing the endpoints of the i-th edge.

The output will be judged correct if the graph satisfies the conditions.

Sample Input 1

3

Sample Output 1

2
1 3
2 3

For every vertex, the sum of the indices of the vertices adjacent to that vertex is 3.

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

N = int(input())

# 完全グラフは惜しい
# 各頂点から自身を除く頂点すべてに辺を貼る
# 誤差をなくすために辺を削る
# 元々十分に辺が張られているので、連結は保たれるだろう

# 補グラフ

# 要素数の偶奇で異なる
# 奇数: [1-6, 2-5, 3-4, 7]
# 偶数: [1-8, 2-7, 3-6, 4-5]

e = [[False for _ in range(N + 1)] for _ in range(N + 1)]
# 1-indexed
for i in range(1, N + 1):
    for j in range(1, N + 1):
        if i == j: continue
        e[i][j] = True
        e[j][i] = True
# 完全グラフを作る

total = -1
if N % 2 == 0:
    total = N + 1
else:
    total = N
# 補グラフのcounterpartを探すのに使用
# total - 自身 = 相方

for i in range(1, N + 1):
    for j in range(1, N + 1):
        if i == j: continue
        cp_i = total - i
        e[i][cp_i] = False
        # 辺を削る

for i in range(1, N + 1):
    for j in range(i + 1, N + 1):
        if e[i][j]:
            print(i, j)