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<bits/stdc++.h>
#define maxN 200005
#define INF 1e18
#define P 1000000007
typedef long long ll;
typedef long double ld;
using namespace std;
int n,a[maxN];
bool vis[maxN];
vector<string> ans;
int pre[maxN];
void cswap(int i,int j)
{
    // cout<<"swap"<<i<<" "<<j<<"\n";
    ans.push_back(to_string(i)+" "+to_string(j));
    // swap(pre[abs(a[i])],pre[abs(a[j])]);
    swap(a[i],a[j]);
    a[i]=-a[i];a[j]=-a[j];
    // for(int i=1;i<=n;++i) cout<<a[i]<<" \n"[i==n];
}
void swap_cycle(int i,int j)
{
    cswap(i,j);
    int cur=i;
    while(a[-a[cur]]>0) cswap(cur,-a[cur]);
    cur=-a[cur];
    while(a[-a[cur]]>0) cswap(cur,-a[cur]);
    cswap(cur,-a[cur]);
}
int main()
{
    // ios::sync_with_stdio(0);
    // cin.tie(0);cout.tie(0);
    cin>>n;
    for(int i=1;i<=n;++i) cin>>a[i];
    // for(int i=1;i<=n;++i) pre[a[i]]=i;
    int p=-1,cntp=0,vp=-1;
    for(int i=1;i<=n;++i){
        if(a[i]==i) {vp=i;continue;}
        if(vis[i]) continue;
        vis[i]=true;
        cntp=1;
        int cur=a[i];
        while(cur!=i){
            vis[cur]=true;
            cntp++;
            cur=a[cur];
        }
        if(p==-1) p=i;
        else{
            swap_cycle(p,i);
            vp=p;
            p=-1;
        }
    }
    // cout<<"here\n";
    if(p!=-1){
        if(cntp==n){
            // cout<<"p=n\n";
            int i=a[1],j=a[a[1]];
            cswap(1,a[1]);
            swap_cycle(i,j);
        }
        else{
            // cout<<p<<" "<<vp<<"\n";
            swap_cycle(p,vp);
        }
    }
    cout<<ans.size()<<"\n";
    for(auto it:ans) cout<<it<<"\n";
}