请问为什么我枚举i ，j作为区间两端点来递推会出问题

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#define N 205
  using namespace std;
char ch1[5][N] , ch2[5][N];
char s[N];
int dp[N][N][5];
int num[N];
int change_num(char ch){
    if(ch == 'W') return 1;
    if(ch == 'I') return 2;
    if(ch == 'N') return 3;
    if(ch == 'G') return 4;
}
char change_ch(int x){
    if(x == 1) return 'W';
    if(x == 2) return 'I';
    if(x == 3) return 'N';
    if(x == 4) return 'G';
}
int main()
{
    for(int i = 1 ; i <= 4 ; i++) cin >> num[i];
    for(int i = 1 ; i <= 4 ; i++)
        for(int j = 1 ; j <= num[i] ; j++) cin >> ch1[i][j] >> ch2[i][j];
    scanf("%s" , s + 1);
    int n = strlen(s + 1);
    for(int i = n - 1 ; i >= 1 ; i -= 2)
        for(int j = i + 1 ; j <= n ; j += 2)
        {
            if(j == i + 1){
                for(int k = 1 ; k <= 4 ; k++)
                    for(int w = 1 ; w <= num[k] ; w++)
                        if(s[i] == ch1[k][w] && s[j] == ch2[k][w]) dp[i][j][k] = 1;
                continue;
            }
            for(int k = i + 1 ; k <= n - 2 ; k += 2){
                for(int p = 1 ; p <= 4 ; p ++)
                    for(int w = 1 ; w <= num[p] ; w++){
                        if(dp[i][k][change_num(ch1[p][w])] && dp[k + 1][j][change_num(ch2[p][w])]) dp[i][j][p] = 1;
                    }
            }
        }
    bool f = 0;
    for(int i = 1 ; i <= 4 ; i++)
        if(dp[1][n][i]){
            cout << change_ch(i);
            f = 1;
        }
    if(!f) cout << "The name is wrong!";
    return 0;
}