#include <iostream>
#include <string>
#include <cctype>

bool isValidExponentialNumber(const std::string& input) {
    // Check if the input string is empty
    if (input.empty()) {
        return false;
    }

    bool hasDecimalPoint = false;
    bool hasExponent = false;
    bool hasSign = false;

    // Iterate through each character in the string
    for (size_t i = 0; i < input.length(); ++i) {
        char ch = input[i];

        // Check for the sign character at the beginning
        if (i == 0 && (ch == '+' || ch == '-')) {
            hasSign = true;
        }
        // Check for digits
        else if (isdigit(ch)) {
            // Digits are allowed
        }
        // Check for the decimal point
        else if (ch == '.') {
            // Decimal point can only occur once and before the exponent
            if (hasDecimalPoint || hasExponent) {
                return false;
            }
            hasDecimalPoint = true;
        }
        // Check for the exponent character
        else if (ch == 'e' || ch == 'E') {
            // Exponent can only occur once and after the sign (if any)
            if (hasExponent || i == 0 || input.length() <= i + 1) {
                return false;
            }
            hasExponent = true;

            // Check for the sign of the exponent
            char nextChar = input[i + 1];
            if (nextChar == '+' || nextChar == '-') {
                ++i; // Skip the exponent sign
            }
        }
        // Invalid character
        else {
            return false;
        }
    }

    // The input is valid if it has at least one digit
    return hasSign || hasDecimalPoint || hasExponent;
}

int main() {
    std::string input;
    std::cout << "Enter a potential exponential number: ";
    std::cin >> input;

    if (isValidExponentialNumber(input)) {
        std::cout << "Valid exponential number." << std::endl;
    } else {
        std::cout << "Invalid exponential number." << std::endl;
    }

    return 0;
}