You are given a positive integer $n$.

Find a sequence of fractions $\frac{a_i}{b_i}$, $i = 1 \ldots k$ (where $a_i$ and $b_i$ are positive integers) for some $k$ such that:

$$ \begin{cases} \text{$b_i$ divides $n$, $1 < b_i < n$ for $i = 1 \ldots k$} \\ \text{$1 \le a_i < b_i$ for $i = 1 \ldots k$} \\ \text{$\sum\limits_{i=1}^k \frac{a_i}{b_i} = 1 - \frac{1}{n}$} \end{cases} $$


-----Input-----

The input consists of a single integer $n$ ($2 \le n \le 10^9$).


-----Output-----

In the first line print "YES" if there exists such a sequence of fractions or "NO" otherwise.

If there exists such a sequence, next lines should contain a description of the sequence in the following format.

The second line should contain integer $k$ ($1 \le k \le 100\,000$) — the number of elements in the sequence. It is guaranteed that if such a sequence exists, then there exists a sequence of length at most $100\,000$.

Next $k$ lines should contain fractions of the sequence with two integers $a_i$ and $b_i$ on each line.


-----Examples-----
Input
2

Output
NO

Input
6

Output
YES
2
1 2
1 3



-----Note-----

In the second example there is a sequence $\frac{1}{2}, \frac{1}{3}$ such that $\frac{1}{2} + \frac{1}{3} = 1 - \frac{1}{6}$.

Difficulty: interview

Starter code:

Solutions:
from math import sqrt

def phi(u):
	ans = u
	for i in range(2, int(sqrt(n)) + 1):
		if u % i == 0:
			while u % i == 0:
				u = u / i
			ans = ans - int(ans / i)
	if n > 1:
		ans = ans - int(ans / n)
	return ans

def binpow(u, a, mod):
	ans = 1
	if a == 0:
		return 1;
	while a > 0:
		if a % 2 == 0:
			u = (u ** 2) % mod
			a = int(a / 2)
		else :
			ans = (ans * u) % mod
			a = a - 1
	return int(ans)

n = int(input())

b1 = 1
b2 = 0
nn = n
for i in range(2, int(sqrt(n)) + 1):
	if n%i == 0 :
		while nn % i == 0:
			b1 = b1 * i
			nn = nn / i
		b2 = int(n / b1)
		break

if b2 < 2:
	print("NO")
	return
a1 = b1 - binpow(b2, phi(b1) - 1, b1)
a2 = b2 - int((a1*b2+1)/b1)
print("YES")
print(2)
print(a1, b1)
print(a2, b2)


#   ==========     //\\       //||     ||====//||
#       ||        //  \\        ||     ||   // ||
#       ||       //====\\       ||     ||  //  ||
#       ||      //      \\      ||     || //   ||
#   ========== //        \\  ========  ||//====|| 
#  code

def egcd(a, b):
    if a == 0 :   
        return b, 0, 1
             
    gcd, x1, y1 = egcd(b % a, a)  

    x = y1 - (b//a) * x1  
    y = x1  
     
    return gcd, x, y

def main():
    n = int(input())
    div = []
    d = set()

    m = n

    i = 2
    while i * i <= n:
        cnt = 0
        while n % i == 0:
            cnt += 1
            n //= i
            d.add(i)
        if cnt > 0:
            div.append((cnt, i))
        i += 1
    
    if n > 1:
        div.append((1, n))
        d.add(n)

    for i in d:
        if i == m:
            d.remove(i)
            break
    
    if len(d) < 2:
        print('NO')
        return
    
    ans1 = 1
    for i in range(div[0][0]):
        ans1 *= div[0][1]
    
    ans2 = 1
    for i in div[1:]:
        for j in range(i[0]):
            ans2 *= i[1]
    
    gcd, x, y = egcd(ans2, -ans1)
    if x < 0 or y < 0:
        gcd, x, y = egcd(ans1, -ans2)
        x,y = y,x
    
    print('YES')
    print(2)

    if ans2 * x + ans1 * y == m - 1:
        print(x, ans1)
        print(y, ans2)
    elif ans2 * (ans1 - x) + ans1 * y == m - 1:
        print(ans1 - x, ans1)
        print(y, ans2)
    elif ans2 * x + ans1 * (ans2 - y) == m - 1:
        print(x, ans1)
        print(ans2 - y, ans2)
    else:
        print(ans1 - x, ans1)
        print(ans2 - y, ans2)

    return

def __starting_point():
    main()
__starting_point()