Problem:
Score : 700 points

Problem Statement

Given is a sequence of N digits a_1a_2\ldots a_N, where each element is 1, 2, or 3.
Let x_{i,j} defined as follows:

x_{1,j} := a_j \quad (1 \leq j \leq N)

x_{i,j} := | x_{i-1,j} - x_{i-1,j+1} | \quad (2 \leq i \leq N and 1 \leq j \leq N+1-i)

Find x_{N,1}.

Constraints

2 \leq N \leq 10^6

a_i = 1,2,3 (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N
a_1a_2\ldotsa_N

Output

Print x_{N,1}.

Sample Input 1

4
1231

Sample Output 1

1

x_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.

x_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.

x_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.

Finally, x_{4,1} = |0-1| = 1, so the answer is 1.

Sample Input 2

10
2311312312

Sample Output 2

0

Solution in PHP7 (7.0.15) (judge verdict: Accepted)

<?php
define("MOD", 100);
$n = intval(trim(fgets(STDIN)));
$s = trim(fgets(STDIN));
$n = strlen($s);
$kigu = 0;
for($i = 0; $i < $n; $i++){
    $dp[$i] = ((int)$s[$i])-1;
    $kigu ^= ($dp[$i]%2) * ((($n-1) & $i) == $i);
}
if($kigu){
    echo 1;
}else{
    if(array_search(1, $dp)!==false){
        echo 0;
    }else{
        $kigu = 0;
        for($i = 0; $i < $n; $i++){
            $dp[$i] = ((int)$s[$i])-1;
            $kigu ^= (($dp[$i]/2)%2) * ((($n-1) & $i) == $i);
        }
        if($kigu){
            echo 2;
        }else{
            echo 0;
        }
    }
}

function chmax(&$a,$b){if($a<$b){$a=$b;return 1;}return 0;}
function chmin(&$a,$b){if($a>$b){$a=$b;return 1;}return 0;}

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 $clean;
}
/**
 * 座圧対象の配列を渡すと以下の値を返す
 * ・圧縮された配列
 * ・復元用のMap
 * ・圧縮用のMap
 **/
function atsu($array){
    $a = array_flip($array);
    $fuku = array_flip($a);
    sort($fuku);
    $atsu = array_flip($fuku);
    foreach($array as $i => $val)$array[$i] = $atsu[$val];
    return [$array, $fuku, $atsu];
}
//配列の最大公約数
function gcdAll($array){
    $gcd = $array[0];
    for($i = 1; $i < count($array); $i++){
        $gcd = gcd($gcd, $array[$i]);
    }
    return $gcd;
}

//最大公約数
function gcd($m, $n){
    if(!$n)return $m;
    return gcd($n, $m % $n);
}

//配列の最小公倍数
function lcmAll($array){
    $lcm = $array[0];
    for($i = 1; $i < count($array); $i++){
        $lcm = lcm($lcm, $array[$i]);
    }
    return $lcm;
}

//最小公倍数
function lcm($a, $b) {
    return $a / gcd($a, $b) * $b;
}
//ビットカウント-1の数を数える
function popcount($x){
    $con = 0;
    while ($x) {
        $x &= $x-1;
        ++$con;
    }
    return $con;
}

function prepareMod($n){
    global $f, $invf;
    $f[0] = $invf[0] = $invf[1] = 1;
    for($i = 1; $i <= $n; $i++)$f[$i] = $f[$i-1]*$i%MOD;
    for($i = 2; $i <= $n; $i++)$invf[$i] = (MOD - intdiv(MOD, $i))*$invf[MOD%$i]%MOD;
    for($i = 2; $i <= $n; $i++)$invf[$i] = $invf[$i]*$invf[$i-1]%MOD;
}
function nCm($n, $m){
    global $f, $invf;
    if($n < 0 || $n - $m < 0)return 0;
    return $f[$n] * $invf[$n-$m] % MOD * $invf[$m] % MOD;
}