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; } real readReal() { return readToken.to!real; } 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; void main() { /* debug {{ bool greedy(in string s) { const n = cast(int)(s.length); int[] xs, ys; for (int i = 0, j; i < n; i = j) { for (j = i; j < n && s[i] == s[j]; ++j) {} if (s[i] == '0') { foreach (k; i .. j) { xs ~= k; } } else { ys ~= i; } } if (xs.length % 2 != 0) { return false; } const len = xs.length / 2; int l; foreach (k; 0 .. len) { for (; ; ) { if (l == ys.length) { return false; } if (xs[k] < ys[l]) { if (ys[l] < xs[len + k]) { ++l; break; } else { return false; } } else { ++l; } } } return true; } enum lim = 16; auto dp = new bool[][lim]; dp[0] = [true]; foreach (n; 1 .. lim) { dp[n] = new bool[1 << n]; foreach (p; 0 .. 1 << n) { foreach (i; 0 .. n) if (p >> i & 1) { if (dp[n - 1][(p & ((1 << i) - 1)) | (p >> (i + 1) << i)]) { dp[n][p] = true; } } foreach (i; 0 .. n - 2) if ((p >> i & 7) == 2) { if (dp[n - 3][(p & ((1 << i) - 1)) | (p >> (i + 3) << i)]) { dp[n][p] = true; } } } int cnt; foreach (p; 0 .. 1 << n) { const s = iota(n).map!(i => "01"[p >> i & 1]).array; if (dp[n][p]) { ++cnt; writeln(s); } const grd = greedy(s); assert(dp[n][p] == grd, format("%s: %s %s", s, dp[n][p], grd)); } stderr.writeln(n, ": ", cnt); stderr.flush; } return; }} //*/ /* 1: 1 2: 1 3: 2 4: 4 5: 7 6: 14 7: 29 8: 57 9: 114 10: 232 11: 465 12: 931 13: 1876 14: 3767 15: 7548 */ try { for (; ; ) { const N = readInt; auto S = readToken; auto crt = new Mint[2][][](N / 2 + 1, N / 2 + 1); auto CRT = new Mint[2][][](N / 2 + 1, N / 2 + 1); crt[0][0][0] = 1; foreach (i; 0 .. N) { auto nxt = new Mint[2][][](N / 2 + 1, N / 2 + 1); auto NXT = new Mint[2][][](N / 2 + 1, N / 2 + 1); const can0 = (S[i] == '?' || S[i] == '0'); const can1 = (S[i] == '?' || S[i] == '1'); foreach (a; 0 .. min(i, N / 2) + 1) foreach (b; 0 .. min(i - a, N / 2) + 1) { static foreach (s; 0 .. 2) if (crt[a][b][s]) { // 0 if (can0 && a + 1 <= N / 2) { nxt[a + 1][b][0] += crt[a][b][s]; } // 1 if (can1) { if (!s && a) { nxt[a - 1][b + 1][1] += crt[a][b][s]; } else { nxt[a][b][1] += crt[a][b][s]; } } // 2 if (can0 && b) { NXT[a][b - 1][0] += crt[a][b][s]; } } } foreach (a; 0 .. min(i, N / 2) + 1) foreach (b; 0 .. min(i - a, N / 2) + 1) { static foreach (s; 0 .. 2) if (CRT[a][b][s]) { // 1 if (can1) { if (!s && a) { NXT[a - 1][b + 1][1] += CRT[a][b][s]; } else { NXT[a][b][1] += CRT[a][b][s]; } } // 2 if (can0 && b) { NXT[a][b - 1][0] += CRT[a][b][s]; } } } crt = nxt; CRT = NXT; } Mint ans; static foreach (s; 0 .. 2) { ans += crt[0][0][s]; ans += CRT[0][0][s]; } writeln(ans); } } catch (EOFException e) { } }