Problem: To learn as soon as possible the latest news about their favourite fundamentally new operating system, BolgenOS community from Nizhni Tagil decided to develop a scheme. According to this scheme a community member, who is the first to learn the news, calls some other member, the latter, in his turn, calls some third member, and so on; i.e. a person with index i got a person with index fi, to whom he has to call, if he learns the news. With time BolgenOS community members understood that their scheme doesn't work sometimes — there were cases when some members didn't learn the news at all. Now they want to supplement the scheme: they add into the scheme some instructions of type (xi, yi), which mean that person xi has to call person yi as well. What is the minimum amount of instructions that they need to add so, that at the end everyone learns the news, no matter who is the first to learn it?

Input

The first input line contains number n (2 ≤ n ≤ 105) — amount of BolgenOS community members. The second line contains n space-separated integer numbers fi (1 ≤ fi ≤ n, i ≠ fi) — index of a person, to whom calls a person with index i.

Output

In the first line output one number — the minimum amount of instructions to add. Then output one of the possible variants to add these instructions into the scheme, one instruction in each line. If the solution is not unique, output any.

Examples

Input

3
3 3 2


Output

1
3 1


Input

7
2 3 1 3 4 4 1


Output

3
2 5
2 6
3 7

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class A {

	static ArrayList<Integer>[] adjList;
	static int V, counter, SCC, dfs_num[], dfs_low[];
	static int[] comp;
	static boolean[] inSCC, vis;
	static Stack<Integer> stack;
	static long memo[];

	static void tarjanSCC() // O(V + E)
	{
		dfs_low = new int[V];
		dfs_num = new int[V];
		stack = new Stack<>();
		inSCC = new boolean[V];
		for (int i = 0; i < V; ++i)
			if (dfs_num[i] == 0)
				tarjanSCC(i);
	}

	static void tarjanSCC(int u) {
		dfs_num[u] = dfs_low[u] = ++counter;
		stack.push(u);

		for (int v : adjList[u]) {
			if (dfs_num[v] == 0)
				tarjanSCC(v);
			if (!inSCC[v])
				dfs_low[u] = Math.min(dfs_low[u], dfs_low[v]);
		}
		if (dfs_num[u] == dfs_low[u]) {
			// SCC found
			SCC++;
			while (true) {
				int v = stack.pop();
				comp[v] = u;
				inSCC[v] = true;
				if (v == u)
					break;
			}
		}
	}

	static boolean dfs(int u, int e) {
//		System.out.println(u + " " + e);
		vis[u] = true;
		if (g[u].size() == 0) {
//			System.out.println(" asdfgh " + u);
			ans.add(new pair(u + 1, e + 1));
			return true;
		}
		boolean f = false;
		for (int v : g[u]) {
			if (!vis[v]) {
				f |= dfs(v, e);
			}
		}
		return f;
	}

	public static void main(String args[]) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);

		int n = sc.nextInt();
		V = n;
		memo = new long[n];
		Arrays.fill(memo, -1);
		adjList = new ArrayList[n];
		g = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			adjList[i] = new ArrayList<>();
			g[i] = new ArrayList<>();
		}

		comp = new int[n];
		vis = new boolean[n];

		for (int i = 0; i < n; i++) {
			int u = sc.nextInt() - 1;
			adjList[i].add(u);
		}
		tarjanSCC();
		int[] indeg = new int[n];
		// Arrays.fill(indeg, -1);
		for (int u = 0; u < n; u++) {
			for (int v : adjList[u]) {
				if (comp[v] != comp[u]) {
					indeg[comp[v]]++;
					g[comp[u]].add(comp[v]);
				} else {
					if (comp[v] != v)
						indeg[v]++;
				}
			}
		}
		arr = new ArrayList<>();
		vis = new boolean[n];
		for (int i = 0; i < indeg.length; i++) {
			if (indeg[i] == 0) {
				arr.add(i);
				// vis[i] = true;
			}
		}
		ans = new ArrayList<>();
		for (int i = 0; i < arr.size() && SCC!=1; i++) {
			boolean f = dfs(arr.get(i), arr.get((i + 1) % arr.size()));
			if (!f) {
				ans.add(new pair(arr.get(i)+1, arr.get((i + 1) % arr.size())+1));
			}
		}
//		System.out.println(Arrays.toString(comp) + " " + arr);
		pw.println(ans.size());
		for (pair p : ans)
			pw.println(p.x + " " + p.y);
		// System.out.println(Arrays.toString(cost));
		// System.out.println(SCC);
		pw.flush();
	}

	static ArrayList<Integer> arr;
	static ArrayList<pair> ans;
	static ArrayList<Integer>[] g;

	///////////////////////////////////////////////////////////////////////////////////////////

	static class tri {
		int x, y, z;

		public tri(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}

	}

	static class pair implements Comparable<pair> {
		int x, y;
		boolean w, l;
		PriorityQueue<Long> pq;

		public pair(boolean a, boolean b) {
			w = a;
			l = b;
		}

		pair(int s, int d) {
			x = s;
			y = d;
		}

		@Override
		public int compareTo(pair p) {
			return Long.compare(x, p.x);
		}

		@Override
		public String toString() {
			return x + " " + y;

		}

	}

	static long mod(long ans, int mod) {
		return (ans % mod + mod) % mod;
	}

	static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}

	static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}

	public static int log(int n, int base) {
		int ans = 0;
		while (n + 1 > base) {
			ans++;
			n /= base;
		}
		return ans;
	}

	static long pow(long b, long e) {
		long ans = 1;
		while (e > 0) {
			if ((e & 1) == 1)
				ans = ((ans * 1l * b));
			e >>= 1;
			{

			}
			b = ((b * 1l * b));
		}
		return ans;
	}

	static long powmod(long r, long e, int mod) {
		long ans = 1;
		r %= mod;
		while (e > 0) {
			if ((e & 1) == 1)
				ans = (int) ((ans * 1l * r) % mod);
			e >>= 1;
			r = (int) ((r * 1l * r) % mod);
		}
		return ans;
	}

	static int ceil(int a, int b) {
		int ans = a / b;
		return a % b == 0 ? ans : ans + 1;
	}

	static long ceil(long a, long b) {
		long ans = a / b;
		return a % b == 0 ? ans : ans + 1;
	}

	static HashMap<Integer, Integer> compress(int a[]) {
		TreeSet<Integer> ts = new TreeSet<>();
		HashMap<Integer, Integer> hm = new HashMap<>();
		for (int x : a)
			ts.add(x);
		for (int x : ts) {
			hm.put(x, hm.size() + 1);
		}
		return hm;
	}

	// Returns nCr % p
	static int C[];

	static int nCrModp(int n, int r, int p) {
		if (r > n - r)
			r = n - r;
		if (C[r] != 0)
			return C[r];
		// The array C is going to store last
		// row of pascal triangle at the end.
		// And last entry of last row is nCr

		C[0] = 1; // Top row of Pascal Triangle

		// One by constructs remaining rows of Pascal
		// Triangle from top to bottom
		for (int i = 1; i <= n; i++) {

			// Fill entries of current row using previous
			// row values
			for (int j = Math.min(i, r); j > 0; j--)

				// nCj = (n-1)Cj + (n-1)C(j-1);
				C[j] = (C[j] + C[j - 1]) % p;
		}
		return C[r];
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public int[] intArr(int n) throws IOException {
			int a[] = new int[n];
			for (int i = 0; i < a.length; i++) {
				a[i] = nextInt();
			}
			return a;
		}

		public long[] longArr(int n) throws IOException {
			long a[] = new long[n];
			for (int i = 0; i < a.length; i++) {
				a[i] = nextLong();
			}
			return a;
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}

	public static void shuffle(int[] times2) {
		int n = times2.length;
		for (int i = 0; i < n; i++) {
			int r = i + (int) (Math.random() * (n - i));
			int tmp = times2[i];
			times2[i] = times2[r];
			times2[r] = tmp;
		}
	}

}