Problem: There are n coins labeled from 1 to n. Initially, coin c_i is on position i and is facing upwards ((c_1, c_2, ..., c_n) is a permutation of numbers from 1 to n). You can do some operations on these coins. 

In one operation, you can do the following:

  * Choose 2 distinct indices i and j.

  * Then, swap the coins on positions i and j.

  * Then, flip both coins on positions i and j. (If they are initially faced up, they will be faced down after the operation and vice versa)




Construct a sequence of at most n+1 operations such that after performing all these operations the coin i will be on position i at the end, facing up.

Note that you do not need to minimize the number of operations.

Input

The first line contains an integer n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of coins.

The second line contains n integers c_1,c_2,...,c_n (1 ≤ c_i ≤ n, c_i ≠ c_j for i≠ j).

Output

In the first line, output an integer q (0 ≤ q ≤ n+1) — the number of operations you used.

In the following q lines, output two integers i and j (1 ≤ i, j ≤ n, i ≠ j) — the positions you chose for the current operation.

Examples

Input


3
2 1 3


Output


3
1 3
3 2
3 1


Input


5
1 2 3 4 5


Output


0

Note

Let coin i facing upwards be denoted as i and coin i facing downwards be denoted as -i.

The series of moves performed in the first sample changes the coins as such:

  * [~~~2,~~~1,~~~3] 
  * [-3,~~~1,-2] 
  * [-3,~~~2,-1] 
  * [~~~1,~~~2,~~~3] 



In the second sample, the coins are already in their correct positions so there is no need to swap.

Solution (in PYTHON3):

Solution:
from sys import stdin, stdout

n=int(stdin.readline())

#make 1-indexed
arr=[0]+list(map(int,stdin.readline().split()))

vis=[0]*(n+1)

ans=[]

def cswap(i,j):
    arr[i],arr[j]=-arr[j],-arr[i]
    ans.append((i,j))
    
def swap_cyc(i,j):
    cswap(i,j)
    
    curr=i
    while (arr[-arr[curr]]>0):
        cswap(curr,-arr[curr])
        
    curr=-arr[curr]
    while (arr[-arr[curr]]>0):
        cswap(curr,-arr[curr])
        
    cswap(curr,-arr[curr])
    
p=-1
for i in range(1,n+1):
    if (vis[i]==1): continue
    if (arr[i]==i): continue
    
    curr=i
    while (True):
        vis[curr]=1
        curr=arr[curr]
        if (curr==i): break
        
    if (p==-1): 
        p=i
    else:
        swap_cyc(p,i)
        p=-1

if (p!=-1):
    can=False
    for i in range(1,n+1):
        if (arr[i]==i):
            swap_cyc(p,i)
            can=True
            break
        
    if (can==False):
        t1,t2=arr[p],arr[arr[p]]
        cswap(p,t1)
        swap_cyc(t1,t2)
            
print(len(ans))
[print(i[0],i[1]) for i in ans]