Problem: PolandBall lives in a forest with his family. There are some trees in the forest. Trees are undirected acyclic graphs with k vertices and k - 1 edges, where k is some integer. Note that one vertex is a valid tree.

There is exactly one relative living in each vertex of each tree, they have unique ids from 1 to n. For each Ball i we know the id of its most distant relative living on the same tree. If there are several such vertices, we only know the value of the one with smallest id among those.

How many trees are there in the forest?

Input

The first line contains single integer n (1 ≤ n ≤ 104) — the number of Balls living in the forest.

The second line contains a sequence p1, p2, ..., pn of length n, where (1 ≤ pi ≤ n) holds and pi denotes the most distant from Ball i relative living on the same tree. If there are several most distant relatives living on the same tree, pi is the id of one with the smallest id.

It's guaranteed that the sequence p corresponds to some valid forest.

Hacking: To hack someone, you should provide a correct forest as a test. The sequence p will be calculated according to the forest and given to the solution you try to hack as input. Use the following format:

In the first line, output the integer n (1 ≤ n ≤ 104) — the number of Balls and the integer m (0 ≤ m < n) — the total number of edges in the forest. Then m lines should follow. The i-th of them should contain two integers ai and bi and represent an edge between vertices in which relatives ai and bi live. For example, the first sample is written as follows:
    
    
      
    5 3  
    1 2  
    3 4  
    4 5  
    

Output

You should output the number of trees in the forest where PolandBall lives.

Interaction

From the technical side, this problem is interactive. However, it should not affect you (except hacking) since there is no interaction.

Examples

Input

5
2 1 5 3 3

Output

2

Input

1
1


Output

1

Note

In the first sample testcase, possible forest is: 1-2 3-4-5. 

There are 2 trees overall.

In the second sample testcase, the only possible graph is one vertex and no edges. Therefore, there is only one tree.

Solution (in JAVA):

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


public class Main_755C {

	private static Scanner sc;
	private static Printer pr;

	private static void solve() {
		int n = sc.nextInt();

		int[] p = sc.nextIntArray(n);

		UnionFind uf = new UnionFind(n);
		for (int i = 0; i < n; i++) {
			uf.unite(i, p[i] - 1);
		}
		
		pr.println(uf.count());
	}

	/**
	 * 互いに素な集合族のためのデータ構造(disjoint-set data structure)
	 */
	static class UnionFind {
//		private int n;
		/** cnt : 異なる集合の数 */
		private int cnt;
		/** 
		 * parent[x] : 0～n-1 の場合、要素xのroot要素
		 *           : -1～-n の場合、自分自身がroot要素、
		 *             -parent[x]でxを含む集合の要素数
		 */
		private int[] parent;
		/** rank[x] : 要素xが属する木の高さ */
		private int[] rank;

		/**
		 * n個の要素数の集合を扱うインスタンスを返す
		 * 
		 * @param n 集合の要素数
		 */
		UnionFind(int n) {
//			this.n = n;
			cnt = n;
			parent = new int[n];
			Arrays.fill(parent, -1);
			rank = new int[n];
			Arrays.fill(rank, 0);
		}

		/**
		 * x が含まれる集合の代表元(root)を返す
		 * 
		 * @param x 対称要素{@literal (0<=x<n)}
		 * @return x が含まれる集合の代表元
		 */
		int find(int x) {
			if (parent[x] < 0) {
				return x;
			} else {
				return parent[x] = find(parent[x]);
			}
		}

		/**
		 * x と y が同じ集合に含まれるのかを返す
		 * 
		 * @param x 対称要素{@literal (0<=x<n)}
		 * @param y 対称要素{@literal (0<=y<n)}
		 * @return 指定された2つの要素が同じ集合に含まれている場合、true
		 */
		boolean same(int x, int y) {
			return find(x) == find(y);
		}

		/**
		 * x が含まれる集合と y が含まれる集合を統合し、これらの和集合を生成する
		 * 
		 * @param x 統合する対称要素{@literal (0<=x<n)}
		 * @param y 統合する対称要素{@literal (0<=y<n)}
		 */
		void unite(int x, int y) {
			x = find(x);
			y = find(y);
			if (x == y) {
				return;
			}

			cnt--;
			// rankが大きい集合をrootにする
			if (rank[x] > rank[y]) {
				parent[x] += parent[y];
				parent[y] = x;
			} else {
				parent[y] += parent[x];
				parent[x] = y;
				if (rank[x] == rank[y]) {
					rank[y]++;
				}
			}

			return;
		}

		/**
		 * x が含まれる集合の要素数を返す
		 * 
		 * @param x 対称要素{@literal (0<=x<n)}
		 * @return x が含まれる集合の要素数
		 */
		int count(int x) {
			return -parent[find(x)];
		}

		/**
		 * n 個の要素を持つ集合がいくつの互いに素な集合に分割されているのかを返す
		 * 
		 * @return 集合全体での互いに素な集合の個数
		 */
		int count() {
			return cnt;
		}
	}

	// ---------------------------------------------------
	public static void main(String[] args) {
		sc = new Scanner(System.in);
		pr = new Printer(System.out);
			
		solve();
			
		pr.close();
		sc.close();
	}

	static class Scanner {
		BufferedReader br;

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

		private boolean isPrintable(int ch) {
			return ch >= '!' && ch <= '~';
		}

		private boolean isCRLF(int ch) {
			return ch == '\n' || ch == '\r' || ch == -1;
		}

		private int nextPrintable() {
			try {
				int ch;
				while (!isPrintable(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}

				return ch;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		String next() {
			try {
				int ch = nextPrintable();
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (isPrintable(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		int nextInt() {
			try {
				// parseInt from Integer.parseInt()
				boolean negative = false;
				int res = 0;
				int limit = -Integer.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Integer.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				int multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		long nextLong() {
			try {
				// parseLong from Long.parseLong()
				boolean negative = false;
				long res = 0;
				long limit = -Long.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Long.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				long multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		float nextFloat() {
			return Float.parseFloat(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			try {
				int ch;
				while (isCRLF(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (!isCRLF(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}
		
		int[] nextIntArray(int n) {
			int[] ret = new int[n];
			for (int i = 0; i < n; i++) {
				ret[i] = sc.nextInt();
			}
			
			return ret;
		}

		long[] nextLongArray(int n) {
			long[] ret = new long[n];
			for (int i = 0; i < n; i++) {
				ret[i] = sc.nextLong();
			}
			
			return ret;
		}

		int[][] nextIntArrays(int m, int n) {
			int[][] ret = new int[m][n];
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					ret[j][i] = sc.nextInt();
				}
			}
			
			return ret;
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
//				throw new NoSuchElementException();
			}
		}
	}

	static class Printer extends PrintWriter {
		Printer(OutputStream out) {
			super(out);
		}
		
		void printInts(int... a) {
			StringBuilder sb = new StringBuilder(32);
			for (int i = 0, size = a.length; i < size; i++) {
				if (i > 0) {
					sb.append(' ');
				}
				sb.append(a[i]);
			}

			println(sb);
		}
		
		void printLongs(long... a) {
			StringBuilder sb = new StringBuilder(64);
			for (int i = 0, size = a.length; i < size; i++) {
				if (i > 0) {
					sb.append(' ');
				}
				sb.append(a[i]);
			}

			println(sb);
		}
		
		void printStrings(String... a) {
			StringBuilder sb = new StringBuilder(32);
			for (int i = 0, size = a.length; i < size; i++) {
				if (i > 0) {
					sb.append(' ');
				}
				sb.append(a[i]);
			}

			println(sb);
		}
	}
}