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 CPP):

Solution:
#include <cstdio>
#include <vector>

int cs[200005];
int inv[200005];

bool vis[200005];

std::vector<std::pair<int,int> > moves;

void flip(int x,int y){
  moves.push_back({x,y});
  std::swap(cs[x],cs[y]);
  std::swap(inv[cs[x]],inv[cs[y]]);
}

void gobble(int x,int y){
  //x and y are in same cycle and have wrong parity
  while(cs[x]!=y){
    flip(x,cs[x]);
  }
  while(cs[y]!=x){
    flip(y,cs[y]);
  }
  flip(x,y);
}

int main(){
  int N;
  scanf("%d",&N);
  for(int i=1;i<=N;i++){
    scanf("%d",&cs[i]);
    inv[cs[i]]=i;
  }
  std::vector<int> cycles;
  for(int i=1;i<=N;i++){
    if(!vis[i]){
      for(int j=i;!vis[j];j=cs[j]){
	vis[j]=true;
      }
      if(i!=cs[i]){
	cycles.push_back(i);
      }
    }
  }
  while(cycles.size()>=2){
    int x=cycles.back();
    cycles.pop_back();
    int y=cycles.back();
    cycles.pop_back();
    flip(x,y);
    gobble(x,y);
  }
  if(cycles.size()>=1){
    int x=cycles.back();
    cycles.pop_back();
    if(cs[cs[x]]==x){
      //length 2
      int y=1;
      while(y==x||y==cs[x]) y++;
      flip(x,y);
      gobble(x,y);
    }else{
      int y=cs[x];
      int z=cs[y];
      flip(y,z);
      flip(x,z);
      gobble(y,z);
    }
  }
  printf("%d\n",(int)moves.size());
  for(auto m:moves){
    printf("%d %d\n",m.first,m.second);
  }
}