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<algorithm>
using namespace std;
const int maxn=200000;

int n,a[maxn+5],id[maxn+5],si[maxn+5],m,c[maxn+5];
int tot,X[maxn+5],Y[maxn+5]; 

inline void Swap(int x,int y) {swap(a[x],a[y]);a[x]=-a[x];a[y]=-a[y];tot++;X[tot]=x;Y[tot]=y;}
void Merge(int x,int y){
	Swap(x,y);
	while (-a[x]!=y) Swap(x,-a[x]);
	while (-a[y]!=x) Swap(y,-a[y]);
	Swap(x,y);
}
int main(){
	scanf("%d",&n);for (int i=1;i<=n;i++) scanf("%d",&a[i]);
	for (int i=1;i<=n;i++) for (int j=i;!id[j];j=a[j]) id[j]=i,si[i]++;
	for (int i=1;i<=n;i++) if (i==id[i] && si[i]>1) c[++m]=i;
	for (int i=1;i<m;i+=2) Merge(c[i],c[i+1]);
	if (m&1){
		int pos;for (int i=1;i<=n;i++) if (i==a[i]) {pos=i;break;}
		if (si[c[m]]==2) Swap(c[m],pos),Swap(pos,-a[pos]),Swap(c[m],pos); else {
			int A=c[m],B=a[c[m]],C=a[a[c[m]]];Swap(A,B);Swap(B,C);
			while (-a[A]!=B) Swap(A,-a[A]);
			while (-a[B]!=A) Swap(B,-a[B]);
			Swap(A,B);
		}
	}
	printf("%d\n",tot);
	for (int i=1;i<=tot;i++) printf("%d %d\n",X[i],Y[i]);
	return 0;
}