Problem p00820 (C++) — buggy submission, verdict: Time Limit Exceeded

#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>

#ifdef __GXX_EXPERIMENTAL_CXX0X__
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>

#ifdef __GXX_EXPERIMENTAL_CXX0X__
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <system_error>
#include <thread>
#include <tuple>
#include <type_traits>
#include <typeindex>
#include <unordered_map>
#include <unordered_set>
#endif

using namespace std;

int main() {
  long long int data[256];
  for (size_t i = 0; i < 256; i++) {
    data[i] = i * i;
  }
  int a;

  while (1) {
    cin >> a;
    if (a == 0) {
      break;
    }
    int count = 0;
    for (size_t i = 0; i < 256; i++) {
      for (size_t j = i; j < 256; j++) {
        for (size_t k = j; k < 256; k++) {
          for (size_t l = k; l < 256; l++) {
            if (data[i] + data[j] + data[k] + data[l] == a) {
              count++;
            } else if (data[i] + data[j] + data[k] + data[l] > a) {
              break;
            }
          }
          if (data[i] + data[j] + data[k] > a) {
            break;
          }
        }
        if (data[i] + data[j] > a) {
          break;
        }
      }
      if (data[i] > a) {
        break;
      }
    }
    cout << count << endl;
  }
  return 0;
}

Error: TLE

Fixed submission:

#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>

#ifdef __GXX_EXPERIMENTAL_CXX0X__
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>

#ifdef __GXX_EXPERIMENTAL_CXX0X__
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <system_error>
#include <thread>
#include <tuple>
#include <type_traits>
#include <typeindex>
#include <unordered_map>
#include <unordered_set>
#endif

using namespace std;

int main() {
  long long int data[256];
  for (size_t i = 0; i < 256; i++) {
    data[i] = i * i;
  }
  int a;

  while (1) {
    cin >> a;
    if (a == 0) {
      break;
    }
    int count = 0;
    for (size_t i = 0; i < 256; i++) {
      for (size_t j = i; j < 256; j++) {
        for (size_t k = j; k < 256; k++) {
          for (size_t l = k; l < 256; l++) {
            if (data[i] + data[j] + data[k] + data[l] == a) {
              count++;
            }
          }
        }
      }
    }
    cout << count << endl;
  }
  return 0;
}