Problem: There are n left boots and n right boots. Each boot has a color which is denoted as a lowercase Latin letter or a question mark ('?'). Thus, you are given two strings l and r, both of length n. The character l_i stands for the color of the i-th left boot and the character r_i stands for the color of the i-th right boot.

A lowercase Latin letter denotes a specific color, but the question mark ('?') denotes an indefinite color. Two specific colors are compatible if they are exactly the same. An indefinite color is compatible with any (specific or indefinite) color.

For example, the following pairs of colors are compatible: ('f', 'f'), ('?', 'z'), ('a', '?') and ('?', '?'). The following pairs of colors are not compatible: ('f', 'g') and ('a', 'z').

Compute the maximum number of pairs of boots such that there is one left and one right boot in a pair and their colors are compatible.

Print the maximum number of such pairs and the pairs themselves. A boot can be part of at most one pair.

Input

The first line contains n (1 ≤ n ≤ 150000), denoting the number of boots for each leg (i.e. the number of left boots and the number of right boots).

The second line contains the string l of length n. It contains only lowercase Latin letters or question marks. The i-th character stands for the color of the i-th left boot.

The third line contains the string r of length n. It contains only lowercase Latin letters or question marks. The i-th character stands for the color of the i-th right boot.

Output

Print k — the maximum number of compatible left-right pairs of boots, i.e. pairs consisting of one left and one right boot which have compatible colors.

The following k lines should contain pairs a_j, b_j (1 ≤ a_j, b_j ≤ n). The j-th of these lines should contain the index a_j of the left boot in the j-th pair and index b_j of the right boot in the j-th pair. All the numbers a_j should be distinct (unique), all the numbers b_j should be distinct (unique).

If there are many optimal answers, print any of them.

Examples

Input


10
codeforces
dodivthree


Output


5
7 8
4 9
2 2
9 10
3 1


Input


7
abaca?b
zabbbcc


Output


5
6 5
2 3
4 6
7 4
1 2


Input


9
bambarbia
hellocode


Output


0


Input


10
code??????
??????test


Output


10
6 2
1 6
7 3
3 5
4 8
9 7
5 1
2 4
10 9
8 10

Solution (in JAVA):

Solution:
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;

/*
 * Author    : joney_000[developer.jaswant@gmail.com]
 * Algorithm : N/A
 * Platform  : Codeforces
 * Ref       : 
 */

public class A {

  private InputStream inputStream;
  private OutputStream outputStream;
  private FastReader in;
  private PrintWriter out;

  private final int BUFFER = 100005;

  private int auxInts[] = new int[BUFFER];
  private long auxLongs[] = new long[1];
  private double auxDoubles[] = new double[1];
  private char auxChars[] = new char[1];
  private final long mod = 1000000000 + 7;
  private final int INF = Integer.MAX_VALUE;
  private final long INF_L = Long.MAX_VALUE / 10;

  public A() {
  }

  public A(boolean stdIO) throws FileNotFoundException {
    // stdIO = false;
    if (stdIO) {
      inputStream = System.in;
      outputStream = System.out;
    } else {
      inputStream = new FileInputStream("input.txt");
      outputStream = new FileOutputStream("output.txt");
    }
    in = new FastReader(inputStream);
    out = new PrintWriter(outputStream);
  }

  void run() throws Exception {
    int n = i();
    String s = s();
    String t = s();
    LinkedList<Integer> []p = new LinkedList[27];
    LinkedList<Integer> []q = new LinkedList[27];
    for(int i = 0; i < 27; i++){
      p[i] = new LinkedList<>();
    }
    for(int i = 0; i < 27; i++) {
      q[i] = new LinkedList<>();
    }
    for(int i = 1; i <= n; i++){
      char x = s.charAt(i - 1);
      char y = t.charAt(i - 1);
      if(x == '?')p[26].add(i);
      else p[x - 'a'].add(i);
      if(y == '?')q[26].add(i);
      else q[y - 'a'].add(i);
    }
    int ans[][] = new int[2][n + 1];
    int idx = 0;
    // int pairs = 0;
    LinkedList<Integer> remainA = new LinkedList<>();
    LinkedList<Integer> remainB = new LinkedList<>();
    
    for(int i = 0; i <= 25; i++){
      int common = Math.min(p[i].size(), q[i].size());
      // pairs += common;
      for(int j = 0; j < common; j++){
        ++idx;
        ans[0][idx] = p[i].removeFirst();
        ans[1][idx] = q[i].removeFirst();
      }
      remainA.addAll(p[i]);
      remainB.addAll(q[i]);  
    }
    // out.write("cnt here : "+idx+"\n");
    while(p[26].size() > 0 && remainB.size() > 0){
      ++idx;
      ans[0][idx] = p[26].removeFirst();
      ans[1][idx] = remainB.removeFirst();
    }
    while (q[26].size() > 0 && remainA.size() > 0) {
      ++idx;
      ans[0][idx] = remainA.removeFirst();
      ans[1][idx] = q[26].removeFirst();
    }
    while (p[26].size() > 0 && q[26].size() > 0) {
      ++idx;
      ans[0][idx] = p[26].removeFirst();
      ans[1][idx] = q[26].removeFirst();
    }
    out.write(""+idx+"\n");
    for(int i = 1; i <= idx; i++){
      out.write(""+ans[0][i]+" "+ans[1][i]+"\n");
    }
  }
  void clear() {

  }

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

  long lcm(long a, long b) {
    if (a == 0 || b == 0)
      return 0;
    return (a * b) / gcd(a, b);
  }

  long mulMod(long a, long b, long mod) {
    if (a == 0 || b == 0)
      return 0;
    if (b == 1)
      return a;
    long ans = mulMod(a, b / 2, mod);
    ans = (ans * 2) % mod;
    if (b % 2 == 1)
      ans = (a + ans) % mod;
    return ans;
  }

  long pow(long a, long b, long mod) {
    if (b == 0)
      return 1;
    if (b == 1)
      return a;
    long ans = pow(a, b / 2, mod);
    ans = (ans * ans);
    if (ans >= mod)
      ans %= mod;

    if (b % 2 == 1)
      ans = (a * ans);
    if (ans >= mod)
      ans %= mod;

    return ans;
  }

  // 20*20 nCr Pascal Table
  long[][] ncrTable() {
    long ncr[][] = new long[21][21];

    for (int i = 0; i <= 20; i++) {
      ncr[i][0] = ncr[i][i] = 1L;
    }

    for (int j = 0; j <= 20; j++) {
      for (int i = j + 1; i <= 20; i++) {
        ncr[i][j] = ncr[i - 1][j] + ncr[i - 1][j - 1];
      }
    }

    return ncr;
  }

  int i() throws Exception {
    return in.nextInt();
  }

  int[] is(int n) throws Exception {
    for (int i = 1; i <= n; i++)
      auxInts[i] = in.nextInt();
    return auxInts;
  }

  long l() throws Exception {
    return in.nextLong();
  }

  long[] ls(int n) throws Exception {
    for (int i = 1; i <= n; i++)
      auxLongs[i] = in.nextLong();
    return auxLongs;
  }

  double d() throws Exception {
    return in.nextDouble();
  }

  double[] ds(int n) throws Exception {
    for (int i = 1; i <= n; i++)
      auxDoubles[i] = in.nextDouble();
    return auxDoubles;
  }

  char c() throws Exception {
    return in.nextCharacter();
  }

  char[] cs(int n) throws Exception {
    for (int i = 1; i <= n; i++)
      auxChars[i] = in.nextCharacter();
    return auxChars;
  }

  String s() throws Exception {
    return in.nextLine();
  }

  BigInteger bi() throws Exception {
    return in.nextBigInteger();
  }

  private void closeResources() {
    out.flush();
    out.close();
    return;
  }

  // IMP: roundoff upto 2 digits
  // double roundOff = Math.round(a * 100.0) / 100.0;
  // or
  // System.out.printf("%.2f", val);

  // print upto 2 digits after decimal
  // val = ((long)(val * 100.0))/100.0;

  public static void main(String[] args) throws java.lang.Exception {

    A driver = new A(true);
    driver.run();
    driver.closeResources();
  }
}

class FastReader {

  private boolean finished = false;

  private InputStream stream;
  private byte[] buf = new byte[4 * 1024];
  private int curChar;
  private int numChars;
  private SpaceCharFilter filter;

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

  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 peek() {
    if (numChars == -1) {
      return -1;
    }
    if (curChar >= numChars) {
      curChar = 0;
      try {
        numChars = stream.read(buf);
      } catch (IOException e) {
        return -1;
      }
      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 == ',') {
        c = read();
      }
      if (c < '0' || c > '9') {
        throw new InputMismatchException();
      }
      res *= 10;
      res += c - '0';
      c = read();
    } while (!isSpaceChar(c));
    return res * sgn;
  }

  public long nextLong() {
    int c = read();
    while (isSpaceChar(c))
      c = read();
    int sgn = 1;
    if (c == '-') {
      sgn = -1;
      c = read();
    }
    long res = 0;
    do {
      if (c < '0' || c > '9') {
        throw new InputMismatchException();
      }
      res *= 10;
      res += c - '0';
      c = read();
    } while (!isSpaceChar(c));
    return res * sgn;
  }

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

  public boolean isSpaceChar(int c) {
    if (filter != null) {
      return filter.isSpaceChar(c);
    }
    return isWhitespace(c);
  }

  public static boolean isWhitespace(int c) {
    return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
  }

  private String readLine0() {
    StringBuilder buf = new StringBuilder();
    int c = read();
    while (c != '\n' && c != -1) {
      if (c != '\r') {
        buf.appendCodePoint(c);
      }
      c = read();
    }
    return buf.toString();
  }

  public String nextLine() {
    String s = readLine0();
    while (s.trim().length() == 0)
      s = readLine0();
    return s;
  }

  public String nextLine(boolean ignoreEmptyLines) {
    if (ignoreEmptyLines) {
      return nextLine();
    } else {
      return readLine0();
    }
  }

  public BigInteger nextBigInteger() {
    try {
      return new BigInteger(nextString());
    } catch (NumberFormatException e) {
      throw new InputMismatchException();
    }
  }

  public char nextCharacter() {
    int c = read();
    while (isSpaceChar(c))
      c = read();
    return (char) c;
  }

  public double nextDouble() {
    int c = read();
    while (isSpaceChar(c))
      c = read();
    int sgn = 1;
    if (c == '-') {
      sgn = -1;
      c = read();
    }
    double res = 0;
    while (!isSpaceChar(c) && c != '.') {
      if (c == 'e' || c == 'E') {
        return res * Math.pow(10, nextInt());
      }
      if (c < '0' || c > '9') {
        throw new InputMismatchException();
      }
      res *= 10;
      res += c - '0';
      c = read();
    }
    if (c == '.') {
      c = read();
      double m = 1;
      while (!isSpaceChar(c)) {
        if (c == 'e' || c == 'E') {
          return res * Math.pow(10, nextInt());
        }
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        m /= 10;
        res += (c - '0') * m;
        c = read();
      }
    }
    return res * sgn;
  }

  public boolean isExhausted() {
    int value;
    while (isSpaceChar(value = peek()) && value != -1)
      read();
    return value == -1;
  }

  public String next() {
    return nextString();
  }

  public SpaceCharFilter getFilter() {
    return filter;
  }

  public void setFilter(SpaceCharFilter filter) {
    this.filter = filter;
  }

  public interface SpaceCharFilter {
    public boolean isSpaceChar(int ch);
  }
}

class Pair implements Comparable<Pair> {
  public int a;
  public int b;

  public Pair() {
    this.a = 0;
    this.b = 0;
  }

  public Pair(int a, int b) {
    this.a = a;
    this.b = b;
  }

  public int compareTo(Pair p) {
    if (this.a == p.a) {
      return this.b - p.b;
    }
    return this.a - p.a;
  }

  @Override
  public String toString() {
    return "a = " + this.a + " b = " + this.b;
  }
}