Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.

In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?

Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.

Input

The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.

The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.

Output

Print a single integer — the minimum number of seconds needed to destroy the entire line.

Examples

Input

3
1 2 1


Output

1


Input

3
1 2 3


Output

3


Input

7
1 4 4 2 3 2 1


Output

2

Note

In the first sample, Genos can destroy the entire line in one second.

In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.

In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1.
import java.io.*;
import java.util.*;
import java.math.*;
import java.text.DecimalFormat;
import java.text.NumberFormat;
 

@SuppressWarnings("unchecked")
public class Main {
      
    int mod = 1000000007;

    public class SegmentTree{

       int n;
       int[] tree;

       SegmentTree(int[] arr){

          this.n = arr.length; 
          this.tree = new int[2 * n];

          for(int i = n; i < 2 * n; i++){
              this.tree[i] = arr[i - n];
          }

          for(int i = n - 1; i >= 1; i--){
              this.tree[i] = Math.min(this.tree[2 * i], this.tree[2 * i + 1]);
          }

       }

       public boolean isIn(int a){

          a += n;
          return tree[a] >= 1000000;

       }

       public int query(int l, int r){

          int res = Integer.MAX_VALUE;
          l = l + n;
          r = r + n;

          while(l < r){

              if(l % 2 == 1){
                  res = Math.min(res, tree[l]); 
                  l++;
              }

              if(r % 2 == 1){
                  r--;
                  res = Math.min(res, tree[r]);
              }

              l /= 2;
              r /= 2;
          }

          return res;
       }

       public void update(int idx, int v){
          
          idx += n; this.tree[idx] += v;
          while(idx > 1){
             idx /= 2;
             this.tree[idx] = Math.min(this.tree[2 * idx], this.tree[2 * idx + 1]);
          }
       }


    }

    public void solve() throws IOException{

       int n = in.nextInt();
       int[] aa = new int[n];
       int[][] dp = new int[n + 1][n + 1];
       for(int i = 0; i < n; i++) aa[i] = in.nextInt();
       for(int i = 0; i <= n - 1; i++) dp[i][i + 1] = 1;

       for(int l = 2; l <= n; l++){ // length of array
          for(int i = 0; i <= n - l; i++){ // starting point, n - l + l = n(not inlclusive)
             dp[i][i + l] = 1 + dp[i + 1][i + l];
             if(aa[i] == aa[i + 1]) dp[i][i + l] = Math.min(dp[i][i + l], 1 + dp[i + 2][i + l]);
             for(int j = 2; j < l; j++){
                if(aa[i] == aa[i + j]){
                  dp[i][i + l] = Math.min(dp[i][i + l], dp[i + 1][i + j] + dp[i + j + 1][i + l]);
                }
             }
          }
       }

       out.println(dp[0][n]);
    }




    FastScanner in;
    PrintWriter out;
    
    static class FastScanner {
 
        BufferedReader br;
        StringTokenizer st;
 
        FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }
 
        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
 
        String nextLine() throws IOException {
            if (st == null || !st.hasMoreTokens())
                return br.readLine();
            StringBuilder result = new StringBuilder(st.nextToken());
            while (st.hasMoreTokens()) {
                result.append(" ");
                result.append(st.nextToken());
            }
            return result.toString();
        }
 
        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
 
        long nextLong() throws IOException {
            return Long.parseLong(next());
        }
 
        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
 
    }
 
    void run() throws IOException {
        in = new FastScanner(System.in);
        out = new PrintWriter(System.out, false);
        solve();
        out.close();
    }
 
    public static void main(String[] args) throws IOException{
        new Main().run();
    }
 
    public void printArr(int[] arr){
        for(int i = 0; i < arr.length; i++){
            out.print(arr[i] + " ");
        }
        out.println();
    }
 
    public long gcd(long a, long b){
        if(a == 0) return b;
        return gcd(b % a, a);
    }

    public boolean isPrime(long num){

        if(num == 0 || num == 1){
            return false;
        }

        for(int i = 2; i * i <= num; i++){
            if(num % i == 0){
                return false;
            }
        }

        return true;
    }

    public class Pair<A, B>{
        public A x; 
        public B y;

        Pair(A x, B y){
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair<?, ?> pair = (Pair<?, ?>) o;
            if (!x.equals(pair.x)) return false;
            return y.equals(pair.y);
        }

        @Override
        public int hashCode() {
            int result = x.hashCode();
            result = 31 * result + y.hashCode();
            return result;
        }

    }

    class Tuple{
        int x; int y; int z;
        Tuple(int ix, int iy, int iz){
            x = ix;
            y = iy;
            z = iz;
        }
    }
}
