why are my getting the wrong answer?

Why are my getting the wrong answer for the “Gift Rift” question.

It works with all of the examples they provided.

#include <iostream>
#include <vector>

using namespace std;

int main() {

	int r, c;
	bool flag = false;
	cin >> r >> c;
	int ** matrix = new int*[r];

	for (int a = 0; a < r; a++){
		matrix[a] = new int[c];
		for (int b = 0; b < c; b++){
			cin >> matrix[a][b];

		}
	}

	pair<int, int> * rows = new pair<int, int>[r];

	for (int a = 0; a < r; a++){
		for (int b = 0; b < c; b++){
			if (rows[a].first > matrix[a][b] || !rows[a].first){
				rows[a].first = matrix[a][b];
				rows[a].second = b;
			}
		}
	}

	pair<int, int> columns;
	
	for (int a = 0; a < c; a++){
		columns.first = -1;
		for (int b = 0; b < r; b++){
			if (matrix[b][a] > columns.first){
				columns.first = matrix[b][a];
				columns.second = b;
			}
		}
		if (columns.first == rows[columns.second].first && rows[columns.second].second == a){
			cout << columns.first << endl;
			flag = true;
			break;
		}
	}

	if (flag == false){
		cout << "GUESS" << endl;
	}

	return 0;
}
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