For problem statement at 1000-1999/1500-1599/1570-1579/1574/problemE.txt this is a correct solution, but verifier at 1000-1999/1500-1599/1570-1579/1574/verifierE.go ends with All tests passed can you fix the verifier? ```go
package main

import (
	"bufio"
	"fmt"
	"os"
)

const MOD = 998244353

func main() {
	in := bufio.NewReader(os.Stdin)
	out := bufio.NewWriter(os.Stdout)
	defer out.Flush()

	var n, m, k int
	// Read n, m, k
	if _, err := fmt.Fscan(in, &n, &m, &k); err != nil {
		return
	}

	// Precompute powers of 2
	limit := n
	if m > limit {
		limit = m
	}
	pow2 := make([]int64, limit+1)
	pow2[0] = 1
	for i := 1; i <= limit; i++ {
		pow2[i] = (pow2[i-1] * 2) % MOD
	}

	// Row state tracking
	// rowBad0[i]: number of cells in row i that violate pattern P0 (where A[i][j] = (i+j)%2)
	// rowBad1[i]: number of cells in row i that violate pattern P1 (where A[i][j] = 1 - (i+j)%2)
	rowBad0 := make([]int, n+1)
	rowBad1 := make([]int, n+1)
	nA_free := n // Number of rows consistent with both patterns (no constraints or empty)
	nA_imp := 0  // Number of rows consistent with neither pattern (impossible)

	// Column state tracking
	// colBad0[j]: number of cells in col j that violate pattern Q0 (where A[i][j] = (i+j)%2)
	// colBad1[j]: number of cells in col j that violate pattern Q1 (where A[i][j] = 1 - (i+j)%2)
	colBad0 := make([]int, m+1)
	colBad1 := make([]int, m+1)
	nB_free := m
	nB_imp := 0

	// Intersection states (specific checkerboard patterns M1 and M2)
	// M1 corresponds to A[i][j] = (i+j)%2 everywhere.
	// M2 corresponds to A[i][j] = 1 - (i+j)%2 everywhere.
	badM1 := 0
	badM2 := 0

	// Grid to store current values: Key is encoded coordinate
	grid := make(map[int64]int)

	updateRow := func(r, val, delta, y int) {
		target := (r + y) % 2
		wasFree := (rowBad0[r] == 0 && rowBad1[r] == 0)
		wasImp := (rowBad0[r] > 0 && rowBad1[r] > 0)

		if val != target {
			rowBad0[r] += delta
		} else {
			rowBad1[r] += delta
		}

		isFree := (rowBad0[r] == 0 && rowBad1[r] == 0)
		isImp := (rowBad0[r] > 0 && rowBad1[r] > 0)

		if wasFree && !isFree {
			nA_free--
		}
		if !wasFree && isFree {
			nA_free++
		}
		if wasImp && !isImp {
			nA_imp--
		}
		if !wasImp && isImp {
			nA_imp++
		}
	}

	updateCol := func(c, val, delta, x int) {
		target := (x + c) % 2
		wasFree := (colBad0[c] == 0 && colBad1[c] == 0)
		wasImp := (colBad0[c] > 0 && colBad1[c] > 0)

		if val != target {
			colBad0[c] += delta
		} else {
			colBad1[c] += delta
		}

		isFree := (colBad0[c] == 0 && colBad1[c] == 0)
		isImp := (colBad0[c] > 0 && colBad1[c] > 0)

		if wasFree && !isFree {
			nB_free--
		}
		if !wasFree && isFree {
			nB_free++
		}
		if wasImp && !isImp {
			nB_imp--
		}
		if !wasImp && isImp {
			nB_imp++
		}
	}

	for i := 0; i < k; i++ {
		var x, y, t int
		fmt.Fscan(in, &x, &y, &t)
		key := (int64(x) << 32) | int64(y)

		// If cell already has a value, remove it first
		if val, ok := grid[key]; ok {
			updateRow(x, val, -1, y)
			updateCol(y, val, -1, x)
			if val != (x+y)%2 {
				badM1--
			} else {
				badM2--
			}
			delete(grid, key)
		}

		// If new operation writes a value (0 or 1)
		if t != -1 {
			grid[key] = t
			updateRow(x, t, 1, y)
			updateCol(y, t, 1, x)
			if t != (x+y)%2 {
				badM1++
			} else {
				badM2++
			}
		}

		// Calculate answer using Principle of Inclusion-Exclusion
		ans := int64(0)
		
		// Ways satisfying Case A (Row condition)
		if nA_imp == 0 {
			ans = (ans + pow2[nA_free]) % MOD
		}
		
		// Ways satisfying Case B (Column condition)
		if nB_imp == 0 {
			ans = (ans + pow2[nB_free]) % MOD
		}
		
		// Subtract Intersection (M1 and M2 are the only valid intersections)
		if badM1 == 0 {
			ans = (ans - 1 + MOD) % MOD
		}
		if badM2 == 0 {
			ans = (ans - 1 + MOD) % MOD
		}

		fmt.Fprintln(out, ans)
	}
}
```