This is a hard version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different.

You are given a string s consisting of n lowercase Latin letters.

You have to color all its characters the minimum number of colors (each character to exactly one color, the same letters can be colored the same or different colors, i.e. you can choose exactly one color for each index in s).

After coloring, you can swap any two neighboring characters of the string that are colored different colors. You can perform such an operation arbitrary (possibly, zero) number of times.

The goal is to make the string sorted, i.e. all characters should be in alphabetical order.

Your task is to find the minimum number of colors which you have to color the given string in so that after coloring it can become sorted by some sequence of swaps. Note that you have to restore only coloring, not the sequence of swaps.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of s.

The second line of the input contains the string s consisting of exactly n lowercase Latin letters.

Output

In the first line print one integer res (1 ≤ res ≤ n) — the minimum number of colors in which you have to color the given string so that after coloring it can become sorted by some sequence of swaps.

In the second line print any possible coloring that can be used to sort the string using some sequence of swaps described in the problem statement. The coloring is the array c of length n, where 1 ≤ c_i ≤ res and c_i means the color of the i-th character.

Examples

Input


9
abacbecfd


Output


2
1 1 2 1 2 1 2 1 2 


Input


8
aaabbcbb


Output


2
1 2 1 2 1 2 1 1


Input


7
abcdedc


Output


3
1 1 1 1 1 2 3 


Input


5
abcde


Output


1
1 1 1 1 1 



import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.net.StandardSocketOptions;
import java.security.cert.CollectionCertStoreParameters;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedHashMap;
import java.util.LinkedList;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.Vector;

import javax.script.ScriptEngine;
import javax.script.ScriptEngineManager;
import javax.script.ScriptException;

public class Main {

    public static int lowerBound(ArrayList<Integer> array, int length, long value) {
        int low = 0;
        int high = length;
        while (low < high) {
            final int mid = (low + high) / 2;
            if (value <= array.get(mid)) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return low;
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    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 void sortbyColumn(int arr[][], int col) {
    // // Using built-in sort function Arrays.sort
    // Arrays.sort(arr, new Comparator<int[]>() {
    //
    // @Override
    // // Compare values according to columns
    // public int compare(final int[] entry1, final int[] entry2) {
    //
    // // To sort in descending order revert
    // // the '>' Operator
    // // if (entry1[col] > entry2[col])
    // // return 1;
    // // else //(entry1[col] >= entry2[col])
    // // return -1;
    // return new Integer(entry1[col]).compareTo(entry2[col]);
    // // return entry1[col].
    // }
    // }); // End of function call sort().
    // }

    static class pair {
        int V, I;

        pair(int v, int i) {
            V = v;
            I = i;
        }
    }

    public static int[] swap(int data[], int left, int right) {
        int temp = data[left];
        data[left] = data[right];
        data[right] = temp;
        return data;
    }

    public static int[] reverse(int data[], int left, int right) {
        while (left < right) {
            int temp = data[left];
            data[left++] = data[right];
            data[right--] = temp;
        }
        return data;
    }

    public static boolean findNextPermutation(int data[]) {
        if (data.length <= 1)
            return false;

        int last = data.length - 2;
        while (last >= 0) {
            if (data[last] < data[last + 1]) {
                break;
            }
            last--;
        }
        if (last < 0)
            return false;

        int nextGreater = data.length - 1;
        for (int i = data.length - 1; i > last; i--) {
            if (data[i] > data[last]) {
                nextGreater = i;
                break;
            }
        }
        data = swap(data, nextGreater, last);
        data = reverse(data, last + 1, data.length - 1);
        return true;
    }

    static long nCr(long n, long r) {
        long x = 1;
        long yu = n - r;
        while (n > r) {
            x = x * n;
            n--;
        }
        while (yu > 0) {
            x /= yu;
            yu--;
        }
        return x;
    }

    /*
     * static boolean prime[] = new boolean[1000007];
     * 
     * public static void sieveOfEratosthenes(int n) {
     * 
     * for (int i = 0; i < n; i++) prime[i] = true; * for (int p = 2; p * p <=
     * n; p++) { // If prime[p] is not changed, then it is a prime if (prime[p]
     * == true) { // Update all multiples of p for (int i = p * p; i <= n; i +=
     * p) prime[i] = false; } }
     * 
     * // Print all prime numbers // for(int i = 2; i <= n; i++) // { //
     * if(prime[i] == true) // System.out.print(i + " "); // } }
     */

    static long power(long fac2, int y, int p) {
        long res = 1;
        fac2 = fac2 % p;
        while (y > 0) {
            if (y % 2 == 1)
                res = (res * fac2) % p;
            fac2 = (fac2 * fac2) % p;
        }
        return res;
    }

    static long modInverse(long fac2, int p) {
        return power(fac2, p - 2, p);
    }

    static boolean isPrime(int n) {
        // Corner cases
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;

        // This is checked so that we can skip
        // middle five numbers in below loop
        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;

        return true;
    }

    public static BigInteger lcmm(String a, String b) {
        BigInteger s = new BigInteger(a);
        BigInteger s1 = new BigInteger(b);
        BigInteger mul = s.multiply(s1);
        BigInteger gcd = s.gcd(s1);
        BigInteger lcm = mul.divide(gcd);
        return lcm;
    }

    static long setBitNumber(long n) {
        if (n == 0)
            return 0;

        long msb = 0;
        while (n != 0) {
            n = n / 2;
            msb++;
        }

        return msb;
    }

    public static void main(String[] args) throws NumberFormatException, IOException, ScriptException {
        FastReader sc = new FastReader();
        PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        // Scanner scn = new Scanner(System.in);
        //
        int n = sc.nextInt();
        String s = sc.next();
        int sum = 0;
        int f = 0;
        ArrayList<Character>max=new ArrayList<>();
        max.add(s.charAt(0));
        StringBuilder sb = new StringBuilder("1 ");
        for (int i = 1; i < n; i++) {
        
       int g=0;
       for(int j=0;j<max.size();j++){
           if(s.charAt(i)>=max.get(j))
           {
               g=1;
               max.set(j,s.charAt(i));
               sb.append((j+1)+" ");
break;
           }

       }
       if(g==0)
       {max.add(s.charAt(i));
       sb.append(max.size()+" ");
       }
        }
        
            pr.println(max.size());
            pr.println(sb);
        

        //
        // coded to perfection by Rohan Mukhija
        pr.flush();
        pr.close();
    }

    static HashMap<Integer, Integer> h = new HashMap<>();

    private static boolean possible(long[] arr, int[] f, long mid, long k) {
        long c = 0;

        for (int i = 0; i < arr.length; i++) {
            if ((arr[i] * f[f.length - i - 1]) > mid) {
                c += (arr[i] - (mid / f[f.length - i - 1]));
            }
        }
        // System.out.println(mid+" "+c);
        if (c <= k)
            return true;
        return false;
    }

}

