Distinct Prime Factors of Product of Array - Problem

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>

int solution(int* nums, int numsSize) {
    // Calculate product of all numbers
    long long product = 1;
    for (int i = 0; i < numsSize; i++) {
        product *= nums[i];
    }
    
    // Find all prime factors of the product
    bool seen[100001] = {false}; // Assuming max prime factor <= 100000
    int count = 0;
    
    // Check for factor 2
    if (product % 2 == 0) {
        if (!seen[2]) {
            seen[2] = true;
            count++;
        }
        while (product % 2 == 0) {
            product /= 2;
        }
    }
    
    // Check for odd factors from 3 onwards
    for (long long i = 3; i * i <= product; i += 2) {
        if (product % i == 0) {
            if (i < 100001 && !seen[i]) {
                seen[i] = true;
                count++;
            }
            while (product % i == 0) {
                product /= i;
            }
        }
    }
    
    // If product > 1, then it's a prime factor
    if (product > 1) {
        if (product < 100001 && !seen[product]) {
            count++;
        } else if (product >= 100001) {
            count++; // Large prime
        }
    }
    
    return count;
}

int main() {
    char line[10000];
    if (fgets(line, sizeof(line), stdin) == NULL) return 1;
    
    // Parse JSON array format [1,2,3]
    int nums[10000];
    int count = 0;
    
    char *start = strchr(line, '[');
    if (start == NULL) return 1;
    start++;
    
    char *end = strchr(start, ']');
    if (end != NULL) *end = '\0';
    
    char *token = strtok(start, ",");
    while (token != NULL && count < 10000) {
        nums[count++] = atoi(token);
        token = strtok(NULL, ",");
    }
    
    int result = solution(nums, count);
    printf("%d\n", result);
    
    return 0;
}