1178_D. Prime Graph_32144
Every person likes prime numbers. Alice is a person, thus she also shares the love for them. Bob wanted to give her an affectionate gift but couldn't think of anything inventive. Hence, he will be giving her a graph. How original, Bob! Alice will surely be thrilled!

When building the graph, he needs four conditions to be satisfied: 

  * It must be a simple undirected graph, i.e. without multiple (parallel) edges and self-loops. 
  * The number of vertices must be exactly n — a number he selected. This number is not necessarily prime. 
  * The total number of edges must be prime. 
  * The degree (i.e. the number of edges connected to the vertex) of each vertex must be prime. 



Below is an example for n = 4. The first graph (left one) is invalid as the degree of vertex 2 (and 4) equals to 1, which is not prime. The second graph (middle one) is invalid as the total number of edges is 4, which is not a prime number. The third graph (right one) is a valid answer for n = 4. 

<image>

Note that the graph can be disconnected.

Please help Bob to find any such graph!

Input

The input consists of a single integer n (3 ≤ n ≤ 1 000) — the number of vertices.

Output

If there is no graph satisfying the conditions, print a single line containing the integer -1.

Otherwise, first print a line containing a prime number m (2 ≤ m ≤ (n(n-1))/(2)) — the number of edges in the graph. Then, print m lines, the i-th of which containing two integers u_i, v_i (1 ≤ u_i, v_i ≤ n) — meaning that there is an edge between vertices u_i and v_i. The degree of each vertex must be prime. There must be no multiple (parallel) edges or self-loops.

If there are multiple solutions, you may print any of them.

Note that the graph can be disconnected.

Examples

Input


4


Output


5
1 2
1 3
2 3
2 4
3 4

Input


8


Output


13
1 2
1 3
2 3
1 4
2 4
1 5
2 5
1 6
2 6
1 7
1 8
5 8
7 8

Note

The first example was described in the statement.

In the second example, the degrees of vertices are [7, 5, 2, 2, 3, 2, 2, 3]. Each of these numbers is prime. Additionally, the number of edges, 13, is also a prime number, hence both conditions are satisfied.

<image>

import sys,os,math
from collections import Counter, defaultdict
import bisect
from sys import stdin, stdout
from itertools import repeat



# n, k = map(int, raw_input().split())
# da = map(int, raw_input().split())
# db = map(int, raw_input().split())


def isp(p):
    for i in range(2, int(math.sqrt(p))+1):
        if p%i==0:
            return False
    return True

def main():
    n = map(int, raw_input().split())[0]
    m = n
    tp = []
    ans = []
    ta = -1
    for i in range(2,1100):
        if isp(i):
            tp.append(i)
            if i>=m and ta == -1:
                ta = i
    # print tp
    i = 1
    while True:
        if m==ta:
            break
        ans.append((i,i+2))
        m += 1
        if m==ta:
            break
        ans.append((i+1, i+3))
        m+=1
        if m==ta:
            break
        i += 4
    # print ta,ans
    print ta
    for i in ans:
        print i[0], i[1]
    for i in range(0, n):
        if i==n-1:
            print i+1, 1
        else:
            print i+1, i+2


main()
