Problem: You are given a string s of length n consisting of lowercase Latin letters. You may apply some operations to this string: in one operation you can delete some contiguous substring of this string, if all letters in the substring you delete are equal. For example, after deleting substring bbbb from string abbbbaccdd we get the string aaccdd.

Calculate the minimum number of operations to delete the whole string s.

Input

The first line contains one integer n (1 ≤ n ≤ 500) — the length of string s.

The second line contains the string s (|s| = n) consisting of lowercase Latin letters.

Output

Output a single integer — the minimal number of operation to delete string s.

Examples

Input


5
abaca


Output


3

Input


8
abcddcba


Output


4

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.FileInputStream;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        FClearTheString solver = new FClearTheString();
        solver.solve(1, in, out);
        out.close();
    }

    static class FClearTheString {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            String str = in.nextLine();
            int[][] dp = new int[n][n];
            for (int i = 0; i < n; i++) dp[i][i] = 1;
            for (int i = 0; i < n - 1; i++) {
                if (str.charAt(i) == str.charAt(i + 1)) dp[i][i + 1] = 1;
                else dp[i][i + 1] = 2;
            }
            for (int len = 3; len <= n; len++) {
                for (int i = 0; i < n; i++) {
                    int j = i - 1 + len;
                    if (j >= n) break;
                    int res1 = dp[i + 1][j] + 1;
                    int res2 = Integer.MAX_VALUE;
                    if (str.charAt(i + 1) == str.charAt(i)) res2 = dp[i + 1][j];
                    if (str.charAt(j) == str.charAt(i)) res2 = Math.min(res2, dp[i + 1][j - 1] + 1);
                    for (int k = i + 2; k < j; k++) {
                        if (str.charAt(i) == str.charAt(k)) res2 = Math.min(res2, dp[i + 1][k - 1] + dp[k][j]);
                    }
                    dp[i][j] = Math.min(res1, res2);
                }
            }
            out.println(dp[0][n - 1]);
            out.flush();
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public InputReader(FileInputStream file) {
            this.stream = file;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = (res << 3) + (res << 1) + c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

    }

    static class OutputWriter {
        private final PrintWriter writer;
        private ArrayList<String> res = new ArrayList<>();
        private StringBuilder sb = new StringBuilder("");

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void println(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                sb.append(objects[i]);
            }
            res.add(sb.toString());
            sb = new StringBuilder("");
        }

        public void close() {
//        writer.flush();
            writer.close();
        }

        public void flush() {
            for (String str : res) writer.printf("%s\n", str);
            res.clear();
            sb = new StringBuilder("");
        }

    }
}