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.PrintWriter;
import java.util.Arrays;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */

public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        FClearTheString solver = new FClearTheString();
        solver.solve(1, in, out);
        out.close();
    }

    static class FClearTheString {
        int[][] dp;
        char[] s;
        ArrayList<Integer>[] arrayLists;

        public char[] reduce(char[] s, int n) {
            char[] ar = new char[n];
            int pointer = 0;
            ar[pointer++] = s[0];
            for (int i = 1; i < n; i++) {
                if (s[i] == ar[pointer - 1]) continue;
                ar[pointer++] = s[i];
            }
            return Arrays.copyOf(ar, pointer);
        }

        public int lowerBound(int index, int value) {
            int low = 0;
            int high = arrayLists[index].size() - 1;
            int ans = -1;
            while (low <= high) {
                int mid = (low + high) / 2;
                if (arrayLists[index].get(mid) >= value) {
                    ans = mid;
                    high = mid - 1;
                } else {
                    low = mid + 1;
                }
            }
            return ans;

        }

        public int findIt(int l, int r) {
            if (l > r) return 0;
            if (dp[l][r] != -1) return dp[l][r];
            int index = lowerBound(s[l] - 'a', l);
            dp[l][r] = findIt(l + 1, r) + 1;
            while (index < arrayLists[s[l] - 'a'].size() && arrayLists[s[l] - 'a'].get(index) <= r) {
                dp[l][r] = Math.min(dp[l][r], findIt(l + 1, arrayLists[s[l] - 'a'].get(index) - 1) + findIt(arrayLists[s[l] - 'a'].get(index), r));
                index++;
            }
            return dp[l][r];
        }

        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            dp = new int[n][n];
            arrayLists = new ArrayList[26];
            for (int i = 0; i < 26; i++) arrayLists[i] = new ArrayList<>();
            for (int i = 0; i < n; i++) Arrays.fill(dp[i], -1);
            s = reduce(in.scanChars(n), n);
            for (int i = 0; i < s.length; i++) arrayLists[s[i] - 'a'].add(i);
            out.println(findIt(0, s.length - 1));
            boolean flag = false;
        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int total;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= total) {
                index = 0;
                try {
                    total = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (total <= 0) return -1;
            }
            return buf[index++];
        }

        public int scanInt() {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

        public char[] scanChars(int n) {
            char[] ar = new char[n];
            int c = scan();
            boolean flag = true;
            while (isWhiteSpace(c)) c = scan();
            ar[0] = (char) c;
            for (int i = 1; i < n; i++) ar[i] = (char) (c = scan());
            return ar;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}