import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } string COLOR(string s = "") { return "\x1b[" ~ s ~ "m"; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } struct ModInt(uint M_) { import std.conv : to; alias M = M_; uint x; this(ModInt a) { x = a.x; } this(uint x_) { x = x_ % M; } this(ulong x_) { x = cast(uint)(x_ % M); } this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; } this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); } ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); } ref ModInt opOpAssign(string op, T)(T a) { static if (is(T == ModInt)) { static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; } else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; } else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } else static if (op == "^^") { if (a < 0) return this = inv()^^(-a); ModInt b = this, c = 1U; for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; } return this = c; } else { return mixin("this " ~ op ~ "= ModInt(a)"); } } ModInt inv() const { uint a = M, b = x; int y = 0, z = 1; for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; } assert(a == 1); return ModInt(y); } ModInt opUnary(string op)() const { static if (op == "+") { return this; } else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; } else static assert(false); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0U); } string toString() const { return x.to!string; } } enum MO = 998244353; alias Mint = ModInt!MO; enum LIM_INV = 2 * 10^^6 + 10; Mint[] inv, fac, invFac; void prepare() { inv = new Mint[LIM_INV]; fac = new Mint[LIM_INV]; invFac = new Mint[LIM_INV]; inv[1] = 1; foreach (i; 2 .. LIM_INV) { inv[i] = -((Mint.M / i) * inv[cast(size_t)(Mint.M % i)]); } fac[0] = invFac[0] = 1; foreach (i; 1 .. LIM_INV) { fac[i] = fac[i - 1] * i; invFac[i] = invFac[i - 1] * inv[i]; } } Mint binom(long n, long k) { if (n < 0) { if (k >= 0) { return (-1)^^(k & 1) * binom(-n + k - 1, k); } else if (n - k >= 0) { return (-1)^^((n - k) & 1) * binom(-k - 1, n - k); } else { return Mint(0); } } else { if (0 <= k && k <= n) { assert(n < LIM_INV); return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)]; } else { return Mint(0); } } } Mint solve(const(int[]) A, const(int[]) B, const(int) N) { debug { writefln("[solve] %s %s %s", A, B, N); } const M = cast(int)(A.length); auto dp = new Mint[N]; dp[1 .. N-1] = Mint(1); foreach (x; 1 .. M) { auto dpSum = new Mint[N + 1]; foreach (y; 0 .. N) dpSum[y + 1] = dpSum[y] + dp[y]; dp[] = Mint(0); // [y0, y1] Mint get(int y0, int y1) { chmax(y0, 0); chmin(y1, N - 1); return (y0 <= y1) ? (dpSum[y1 + 1] - dpSum[y0]) : Mint(0); } const f = (abs(A[x - 1] - B[x ]) > N); const g = (abs(A[x ] - B[x - 1]) > N); foreach (y; 1 .. N-1) { dp[y] = get(g ? (y - 1) : 0, f ? (y + 1) : (N-1)); } debug { writefln("f = %s, g = %s, dp = %s", f, g, dp); } } const ret = dp.sum; return ret; } void main() { prepare; /* debug {{ // 1 wall in each row enum INF = 10^^9; foreach (m; 1 .. 5 + 1) foreach (n; 3 .. 7 + 1) { auto freq = new int[m * n]; foreach (p; 0 .. (n - 2)^^m) { const ys = iota(m).map!(x => (1 + p / (n - 2)^^(m-1-x) % (n - 2))).array; auto wall = new bool[][](m, n); foreach (x; 0 .. m) wall[x][ys[x]] = true; const U = m * n; auto dist = new int[][](U, U); foreach (u; 0 .. U) { dist[u][] = INF; dist[u][u] = 0; } void ae(int x0, int y0, int x1, int y1) { const u = x0 * n + y0; const v = x1 * n + y1; chmin(dist[u][v], 1); chmin(dist[v][u], 1); } foreach (x; 0 .. m) foreach (y; 0 .. n) if (!wall[x][y]) { if (x + 1 < m && !wall[x + 1][y]) ae(x, y, x + 1, y); if (y + 1 < n && !wall[x][y + 1]) ae(x, y, x, y + 1); } foreach (w; 0 .. U) foreach (u; 0 .. U) foreach (v; 0 .. U) chmin(dist[u][v], dist[u][w] + dist[w][v]); int mn = INF; foreach (x0; 0 .. m) foreach (x1; 0 .. m) chmin(mn, dist[x0 * n + 0][x1 * n + (n - 1)]); if (mn < INF) { ++freq[mn]; assert(mn == n); } } writeln(m, " ", n, ": ", freq); } }} //*/ try { for (; ; ) { const M = readInt; const N = readInt; auto A = new int[][](M, N); foreach (y; 0 .. N) A[0 ][y] = readInt; foreach (x; 1 .. M-1) { A[x][0 ] = readInt; A[x][N-1] = readInt; } foreach (y; 0 .. N) A[M-1][y] = readInt; debug { writeln("A = ", A); } bool ok = true; foreach (y; 0 .. N - 1) ok = ok && (abs(A[0 ][y] - A[0 ][y + 1]) <= 1); foreach (y; 0 .. N - 1) ok = ok && (abs(A[M-1][y] - A[M-1][y + 1]) <= 1); foreach (x; 0 .. M - 1) ok = ok && (abs(A[x][0 ] - A[x + 1][0 ]) <= 1); foreach (x; 0 .. M - 1) ok = ok && (abs(A[x][N-1] - A[x + 1][N-1]) <= 1); if (ok) { int[] xs, ys; foreach (x; 0 .. M) if (abs(A[x][0] - A[x][N-1]) > N - 1) xs ~= x; foreach (y; 0 .. N) if (abs(A[0][y] - A[M-1][y]) > M - 1) ys ~= y; debug { writefln("M = %s, N = %s; xs = %s, ys = %s", M, N, xs, ys); } const xsLen = cast(int)(xs.length); const ysLen = cast(int)(ys.length); Mint ans = 1; if (xsLen) { if (ysLen) { assert(false); } else { for (int i = 0, j; i < xsLen; i = j) { for (; j < xsLen && xs[i] - i == xs[j] - j; ++j) {} int[] as, bs; foreach (k; i .. j) { as ~= A[xs[k]][0]; bs ~= A[xs[k]][N-1]; } ans *= solve(as, bs, N); } } } else { if (ysLen) { for (int i = 0, j; i < ysLen; i = j) { for (; j < ysLen && ys[i] - i == ys[j] - j; ++j) {} int[] as, bs; foreach (k; i .. j) { as ~= A[0][ys[k]]; bs ~= A[M-1][ys[k]]; } ans *= solve(as, bs, M); } } else { // } } writeln(ans); } else { writeln(-1); } } } catch (EOFException e) { } }