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.util.*;
import java.util.logging.Level;
import java.io.*;

public class tr0 {
	static PrintWriter out;
	static StringBuilder sb;
	static final double EPS = 1e-9;
	static long mod = 1000000007;
	static int inf = (int) 1e9 + 2;
	static long[] fac;
	static int[] si;
	static ArrayList<Integer> primes;
	static ArrayList<Integer>[] ad;
	static ArrayList<qu>[] d;
	static edge[] ed;
	static int[] l, ch;
	static int[] occ;
	static long[][] adjMatrix;
	static Queue<Integer>[] can;
	static String s;
	static int[][] memo, P;
	static int n, k;
	static int[] a, pa;
	static boolean[] t;
	static HashMap<Integer, Integer> pri;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		int n=sc.nextInt();
		String s=sc.nextLine();
		int []a=new int[26];
		int []ans=new int [n];
		int max=0;
		for(int i=0;i<n;i++) {
			int ma=0;
			for(int j=s.charAt(i)-'a'+1;j<26;j++)
				ma=Math.max(ma, a[j]);
			ans[i]=ma+1;
			max=Math.max(max, ans[i]);
			a[s.charAt(i)-'a']=Math.max(ans[i],a[s.charAt(i)-'a'] );
		}
		out.println(max);
		for(int i=0;i<n;i++)
			out.print(ans[i]+" ");
		out.flush();
	}
	static class qu implements Comparable<qu> {
		int a;
		int b;
		int w;

		qu(int aa, int bb, int cc) {
			a = aa;
			b = bb;
			w = cc;
		}

		public String toString() {
			return a + " " + b + " " + w;
		}

		public int compareTo(qu o) {
			if (a == o.a)
				return b - o.b;
			return a - o.a;
		}
	}

	static class seg implements Comparable<seg> {
		int a;
		int b;
		int l;
		int r;
		int bit;

		seg(int s, int e, int x, int y, int bi) {
			a = s;
			b = e;
			l = x;
			r = y;
			bit = bi;
		}

		public String toString() {
			return a + " " + b + " " + l + " " + r + " " + bit;
		}

		public int compareTo(seg o) {
			// if(a==o.a)
			return bit - o.bit;
			// return
		}
	}

	static class pair implements Comparable<pair> {
		long to;
		long number;

		pair(long t, long n) {
			number = n;
			to = t;
		}

		public String toString() {
			return to + " " + number;
		}

		@Override
		public int compareTo(pair o) {
			if (o.to < to)
				return 1;
			return -1;
		}

	}

	static long modPow(long a, long e)

	{
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1)
				res = (res * a) % mod;
			a = (a * a) % mod;
			e >>= 1;
		}
		return res;
	}

	static long inver(long x) {
		long a = x;
		long e = (mod - 2);
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1) {
				res = ((1l * res * a) % mod);
			}
			a = ((1l * a * a) % mod);
			e >>= 1;
		}
		return res % mod;
	}

	static class edge implements Comparable<edge> {
		int from;
		int to;
		int number;

		edge(int f, int t, int n) {
			from = f;
			to = t;
			number = n;
		}

		public String toString() {
			return from + " " + to + " " + number;
		}

		public int compareTo(edge f) {
			return f.number - number;
		}
	}

	static void seive(int N) {
		si = new int[N];
		primes = new ArrayList<>();
		si[1] = 1;
		for (int i = 2; i < N; i++) {
			if (si[i] == 0) {
				si[i] = i;
				primes.add(i);
			}
			for (int j = 0; j < primes.size() && primes.get(j) <= si[i] && (i * primes.get(j)) < N; j++)
				si[primes.get(j) * i] = primes.get(j);
		}
	}

	static long fac(int n) {
		if (n == 0)
			return fac[n] = 1;
		if (n == 1)
			return fac[n] = 1;
		long ans = 1;
		for (int i = 1; i <= n; i++)
			fac[i] = ans = (i % mod * ans % mod) % mod;
		return ans % mod;
	}

	static long gcd(long a, long b) {

		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	static class unionfind {
		int[] p;
		int[] size;
		int[] max;
		int num;

		unionfind(int n) {
			p = new int[n];
			size = new int[n];
			max = new int[n];
			for (int i = 0; i < n; i++) {
				p[i] = i;
				max[i] = i;
			}
			Arrays.fill(size, 1);
			num = n;
		}

		int findSet(int v) {
			if (v == p[v])
				return v;

			max[v] = Math.max(max[v], max[p[v]]);

			p[v] = findSet(p[v]);

			max[v] = Math.max(max[v], max[p[v]]);

			return p[v];
		}

		boolean sameSet(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			return false;
		}

		int max() {
			int max = 0;
			for (int i = 0; i < size.length; i++)
				if (size[i] > max)
					max = size[i];
			return max;
		}

		boolean combine(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			// System.out.println(num+" ppp");
			num--;
			if (size[a] > size[b]) {
				p[b] = a;
				max[a] = Math.max(max[a], max[b]);
				size[a] += size[b];

			} else {
				p[a] = b;
				max[b] = Math.max(max[a], max[b]);
				size[b] += size[a];
			}
			return false;
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

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

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}