text justification dynamic programming c++

I'm trying to understand the text justification problem the program must return the minimum badness but it return negative value i don't know why

#include <bits/stdc++.h>
using namespace std;

string text[4] = {"-1", "sayed", "play", "chess"};
int N = 4;
int width = 10;
//int store[4];

int badness(int i, int j){
    int sum = 0;
    for(i ; i <= j ; i++)
        sum += text[i].size();
    if(j-i > 1 ) sum += j - i; 
    return pow((width - sum),3);
}
int jt(int i){
    if (i == N + 1) return 0;
    int m = (int)1e8;
    for(int j = i + 1 ; j <= N + 1 ; j++)  //why to N+1 and why we start from i+1
        m = min(m, jt(j)+badness(i, j-1));
    return m;
}

int main(){
    cout << jt(0) << endl; 
}