Ruudukko

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

//console.log(n, grid.length, grid.at(-1).length)

if (n !== grid.length) throw new Error("input reading... really?");

const key = (r, c) => `${r},${c}`;
const memo = new Map();

function routes(r, c) {
  const k = key(r, c);
  if (memo.has(k)) return memo.get(k);

  const v = grid[r][c];
  const next = [];
  for (let a = 0; a < n; a++) {
    if (grid[a][c] < v) next.push([a, c]);
    if (grid[r][a] < v) next.push([r, a]);
  }

  let s = BigInt(next.length);
  for (const [r2, c2] of next) {
    s += routes(r2, c2);
  }

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

let sum = BigInt(n**2);

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

// console.log(memo)
console.log((sum % ((10n**9n)+7n)).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