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:
def swap(i, j):
    graph[i], graph[j] = -graph[j], -graph[i]
    ans.append((i, j))

def solve_pair(x, y):
    swap(x, y)
    i = x
    while (graph[-graph[i]] > 0):
        swap(i, -graph[i])
    i = -graph[i]
    while (graph[-graph[i]] > 0):
        swap(i, -graph[i])
    swap(i, -graph[i])

n = int(input())
j = 1
graph = [0]
solved = set()
for i in input().split():
    graph.append(int(i))
    if (int(i) == j):
        solved.add(j)
    j+=1

ans = []
cycles = set()

for x in range(1, n+1):
    if not (x in solved):
        i = x
        solved.add(i)
        i = graph[i]
        while (i != x):
            solved.add(i)
            i = graph[i]
        cycles.add(i)

while (len(cycles) > 1):
    solve_pair(cycles.pop(), cycles.pop())

if (len(cycles) == 1):
    j = 1
    while (not (j == n+1 or j == graph[j])):
        j+=1
    
    if (j != n+1):
        solve_pair(j, cycles.pop())
    else:
        i, j = graph[1], graph[graph[1]]
        swap(1, graph[1])
        solve_pair(i, j)

print(len(ans))
for i in ans:
    print(i[0], i[1])