Problem:
Score : 500 points

Problem Statement

You are given a string S of length N consisting of lowercase English letters.

Process Q queries of the following two types:

Type 1: change the i_q-th character of S to c_q. (Do nothing if the i_q-th character is already c_q.)

Type 2: answer the number of different characters occurring in the substring of S between the l_q-th and r_q-th characters (inclusive).

Constraints

N, Q, i_q, l_q, and r_q are integers.

S is a string consisting of lowercase English letters.

c_q is a lowercase English letter.

1 \leq N \leq 500000

1 \leq Q \leq 20000

|S| = N

1 \leq i_q \leq N

1 \leq l_q \leq r_q \leq N

There is at least one query of type 2 in each testcase.

Input

Input is given from Standard Input in the following format:

N
S
Q
Query_1
\vdots
Query_Q

Here, Query_i in the 4-th through (Q+3)-th lines is one of the following:

1 i_q c_q

2 l_q r_q

Output

For each query of type 2, print a line containing the answer.

Sample Input 1

7
abcdbbd
6
2 3 6
1 5 z
2 1 1
1 4 a
1 7 d
2 1 7

Sample Output 1

3
1
5

In the first query, cdbb contains three kinds of letters: b , c , and d, so we print 3.

In the second query, S is modified to abcdzbd.

In the third query, a contains one kind of letter: a, so we print 1.

In the fourth query, S is modified to abcazbd.

In the fifth query, S does not change and is still abcazbd.

In the sixth query, abcazbd contains five kinds of letters: a, b, c, d, and z, so we print 5.

Solution in PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
$n = intval(fgets(STDIN));
$str = trim(fgets(STDIN));
$Q = intval(fgets(STDIN));

for($i = 0; $i < 26; $i++){
  $array[$i] = array_fill(0, $n, 0);
}
for($i = 0; $i < $n; $i++){
  $array[ord($str[$i])-97][$i]++;
}
for($i = 0; $i < 26; $i++){
  $seg[$i] = new SegTree($array[$i]);
}

while($Q--){
  list($q, $a, $b) = explode(" ", trim(fgets(STDIN)));
  $a--;$b--;
  if($q == "1"){
    if($str[$a] != $b){
      $seg[ord($str[$a])-97]->add($a, -1);
      $seg[ord($b)-97]->add($a,  1);
      $str[$a] = $b;
    }
  }else{
    $c = 0;
    for($i = 0; $i < 26; $i++){
      $c += $seg[$i]->sumBetween($a, $b) > 0;
    }
    echo $c,"\n";
  }
}

class SegTree{
  public $tree;
  public $bits;
  function __construct($n){
    if(is_array($n)){
      $this->bits = max(1, ceil(log(count($n))/log(2)));
      $this->tree[$this->bits] = $n;
      for($i = count($n), $I = 2**$this->bits; $i < $I; ++$i){
        $this->tree[$this->bits][] = 0;  
      }
      for($i = $this->bits - 1; $i >= 1 ; --$i){
        $treei = &$this->tree[$i];
        $treeip = $this->tree[$i+1];
        for($j = 0, $J = 2**$i; $j < $J; $j++){
          $treei[$j] = $treeip[$j*2] + $treeip[$j*2+1];  
        }
      }
    }else{
      $this->bits = max(1, ceil(log($n)/log(2)));
      for($i = 1; $i <= $this->bits; ++$i){
        $this->tree[$i] = array_fill(0, 2**$i, 0);
      }
    }
  }
  function add($i, $amount = 1){
    for($j = $this->bits; $j >= 1; --$j){
      $this->tree[$j][$i] += $amount;
      $i>>=1;
    }
  }
  function sumLTE($t){return $this->sumLT($t+1);}
  function sumLT($t){
    $ret = 0;
    for($i = $this->bits; $i >= 1 ; --$i){
        if(($t >> ($i-1)) & 1){
          $ret += $this->tree[$this->bits - $i + 1][($t >> ($i-1)) ^ 1];
        }
    }
    return $ret;
  }
  function sum(){
    return array_sum($this->tree[1]);
  }
  function sumBetween($f, $t){
    return $this->sumLT($t+1) - $this->sumLT($f);
  }
}

function o(...$val){
    if(count($val)==1)$val = array_shift($val);
    $trace = debug_backtrace();
    echo $trace[0]['line'].")";
    if(is_array($val)){
        if(count($val) == 0){
            echo "empty array";
        }elseif(!is_array(current($val))){
            echo "array: ";
            echo implode(" ", addIndex($val))."\n";
        }else{
            echo "array:array\n";
            if(isCleanArray($val)){
                foreach($val as $row)echo implode(" ", addIndex($row))."\n";
            }else{
                foreach($val as $i => $row)echo "[".$i."] ".implode(" ", addIndex($row))."\n";
            }
        }
    }else{
        echo $val."\n";
    }
}
function addIndex($val){
    if(!isCleanArray($val)){
        $val = array_map(function($k, $v){return $k.":".$v;}, array_keys($val), $val);
    }
    return $val;
}
function isCleanArray($array){
    $clean = true;
    $i = 0;
    foreach($array as $k => $v){
        if($k != $i++)$clean = false;
    }
    return $clean;
}