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)); } enum M = (BigInt(1) << 126) - 137; alias Pair = Tuple!(BigInt, "x", BigInt, "y"); enum IDENTITY = Pair(BigInt(1), BigInt(0)); Pair mul(Pair f, Pair g) { return Pair((f.x * g.x) % M, (f.y + f.x * g.y) % M); } Pair power(Pair f, long e) { Pair g = IDENTITY; for (; ; f = mul(f, f)) { if (e & 1) g = mul(g, f); if (!(e >>= 1)) return g; } } void main() { import std.random; auto rng = Random(unpredictableSeed); const B = (BigInt(uniform(0UL, 1UL << 63)) | BigInt(uniform(0UL, 1UL << 63)) << 63) % M; debug writeln("M = ", M, ", B = ", B); try { for (; ; ) { const K = readInt; auto S = new string[K]; auto T = new long[K]; foreach (k; 0 .. K) { S[k] = readToken; T[k] = readLong; } BigInt solve() { debug writeln(S, " ", T); Pair prod = IDENTITY; foreach (k; 0 .. K) { Pair p = IDENTITY; foreach (s; S[k]) { p = mul(p, Pair(B, BigInt(cast(long)(s)))); } p = power(p, T[k]); prod = mul(prod, p); } debug writeln(prod); return prod.y; } const res0 = solve; foreach (k; 0 .. K) { S[k] = S[k].dup.reverse.idup; } S.reverse; T.reverse; const res1 = solve; writeln((res0 == res1) ? "Yes" : "No"); } } catch (EOFException e) { } }