Detect Capital LeetCode solution in C++

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class Solution {
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 public:
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  bool detectCapitalUse(string word) {
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    int n = word.size();
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    // if the first letter of the string is lower-case
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    if (islower(word[0])) {
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      int c = 0;
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      for (int i = 0; i < n; i++) {
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        if (islower(word[i])) {
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          c++;
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        }
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      }
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      // total lower-case count must be equal to the size of the string
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      if (c == n) {
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        return true;
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      }
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      return false;
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    }
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    // if the first letter of the string is upper-case.
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    else {
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      int c = 0;
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      for (int i = 0; i < n; i++) {
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        if (isupper(word[i])) {
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          c++;
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        }
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      }
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      // count of total upper-case letters must be equal to 1 or to the size of
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      // the string.
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      if (c == 1 or c == n) {
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        return true;
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      }
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      // in all other cases, return false.
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      return false;
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    }
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  }
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};