<p>Let&#39;s say a positive integer is a <strong>super-palindrome</strong> if it is a palindrome, and it is also the square of a palindrome.</p>

<p>Given two positive integers <code>left</code> and <code>right</code> represented as strings, return <em>the number of <strong>super-palindromes</strong> integers in the inclusive range</em> <code>[left, right]</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> left = &quot;4&quot;, right = &quot;1000&quot;
<strong>Output:</strong> 4
<strong>Explanation</strong>: 4, 9, 121, and 484 are superpalindromes.
Note that 676 is not a superpalindrome: 26 * 26 = 676, but 26 is not a palindrome.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> left = &quot;1&quot;, right = &quot;2&quot;
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= left.length, right.length &lt;= 18</code></li>
	<li><code>left</code> and <code>right</code> consist of only digits.</li>
	<li><code>left</code> and <code>right</code> cannot have leading zeros.</li>
	<li><code>left</code> and <code>right</code> represent integers in the range <code>[1, 10<sup>18</sup> - 1]</code>.</li>
	<li><code>left</code> is less than or equal to <code>right</code>.</li>
</ul>

vector<uint64_t> value {
    0, 1, 4, 9, 121, 484, 676, 10201, 12321, 14641, 40804, 44944, 69696, 94249, 698896, 1002001, 1234321, 
    4008004, 5221225, 6948496, 100020001, 102030201, 104060401, 121242121, 123454321, 125686521, 400080004, 
    404090404, 522808225, 617323716, 942060249, 10000200001, 10221412201, 12102420121, 12345654321, 
    40000800004, 637832238736, 1000002000001, 1002003002001, 1004006004001, 1020304030201, 1022325232201, 
    1024348434201, 1086078706801, 1210024200121, 1212225222121, 1214428244121, 1230127210321, 1232346432321, 
    1234567654321, 1615108015161, 4000008000004, 4004009004004, 4051154511504, 5265533355625, 9420645460249, 
    100000020000001, 100220141022001, 102012040210201, 102234363432201, 121000242000121, 121242363242121, 
    123212464212321, 123456787654321, 123862676268321, 144678292876441, 165551171155561, 400000080000004, 
    900075181570009, 4099923883299904, 10000000200000001, 10002000300020001, 10004000600040001, 10020210401202001, 
    10022212521222001, 10024214841242001, 10201020402010201, 10203040504030201, 10205060806050201, 
    10221432623412201, 10223454745432201, 12100002420000121, 12102202520220121, 12104402820440121, 
    12120030703002121, 12122232623222121, 12124434743442121, 12321024642012321, 12323244744232321, 
    12341234943214321, 12343456865434321, 12345678987654321, 40000000800000004, 40004000900040004, 94206450305460249,
};

class Solution {
public:
    int superpalindromesInRange(string L, string R) {
        auto l = lower_bound(value.begin(), value.end(), stoull(L));
        auto r = upper_bound(value.begin(), value.end(), stoull(R));
        int res = 0;
        for (;l != r; ++l) {
            int64_t v = *l;
            int64_t root = round(sqrt(v));
            string s1 = to_string(root);
            string s2 = s1;
            reverse(s2.begin(), s2.end());
            if (s2 == s1) ++res;
        }
        return res;
    }
};    
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