Ruudukko

const [[n], ...grid] = require("fs").readFileSync(0, "utf8").trim().split("\n").map(l => l.trim().split(" ").map(Number));

const MOD = (10 ** 9) + 7;

const key = /** @type {(r: number, c: number) => string} */ (r, c) => `${r},${c}`;
const memo = new Map();

/**
 * @param {number} r 
 * @param {number} c 
 * @returns {number}
 */
function routes(r, c) {
  const k = key(r, c);
  if (memo.has(k)) return memo.get(k);

  const v = grid[r][c];
  let s = 0;
  for (let a = 0; a < n; a++) {
    if (grid[a][c] < v) s += 1 + routes(a, c);
    if (grid[r][a] < v) s += 1 + routes(r, a);
    s %= MOD;
  }

  memo.set(k, s);
  return s;
}

let sum = n ** 2;

for (let r = 0; r < n; r++) {
  for (let c = 0; c < n; c++) {
    sum += routes(r, c);
    sum %= MOD;
  }
}

console.log(sum.toString());

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 1, 2, 3

Verdict: ACCEPTED

Test 4

Group: 2, 3

Verdict: ACCEPTED

Test 5

Group: 2, 3

Verdict: ACCEPTED

Test 6

Group: 2, 3

Verdict: ACCEPTED

Test 7

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 8

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 9

Group: 3

Verdict: TIME LIMIT EXCEEDED