import std.conv, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.container, std.math, std.numeric, std.range, 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; } void chmin(T)(ref T t, in T f) { if (t > f) t = f; } void chmax(T)(ref T t, in T f) { if (t < f) t = f; } int binarySearch(T)(in T[] as, in bool delegate(T) test) { int low = -1, upp = cast(int)(as.length); for (; low + 1 < upp; ) { int mid = (low + upp) >> 1; (test(as[mid]) ? low : upp) = mid; } return upp; } int lowerBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a < val)); } int upperBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a <= val)); } int N; long[] A, X, Y; void main() { try { for (; ; ) { N = readInt(); A = new long[N]; foreach (i; 0 .. N) { A[i] = readLong(); } X = new long[N]; foreach (i; 0 .. N) { X[i] = readLong(); } Y = new long[N]; foreach (i; 0 .. N) { Y[i] = readLong(); } debug { auto dp = new long[N]; foreach (i; 0 .. N) { dp[i] = (X[0] - A[i])^^2 + (Y[0] - 0)^^2; foreach (j; 1 .. i + 1) { chmin(dp[i], dp[j - 1] + (X[j] - A[i])^^2 + (Y[j] - 0)^^2); } } writeln(dp); } /* dp[i] = min{ dp[j - 1] + (X[j] - A[i])^2 + (Y[j] - 0)^2 | 0 <= j <= i } = min{ (dp[j - 1] + X[j]^2 + Y[j]^2) - (2 X[j]) A[i] } + A[i]^2 */ long ans; auto q = new Tuple!(long, long)[N + 1]; int qHead, qTail; foreach (i; -1 .. N) { long z; if (i == -1) { z = 0; } else { for (; qTail - qHead >= 2 && q[qHead][0] - q[qHead][1] * A[i] >= q[qHead + 1][0] - q[qHead + 1][1] * A[i]; ++qHead) {} z = q[qHead][0] - q[qHead][1] * A[i] + A[i]^^2; } debug { writeln(i, " ", z); } if (i == N - 1) { ans = z; } else { const p = tuple(z + X[i + 1]^^2 + Y[i + 1]^^2, 2 * X[i + 1]); // ([-2][0] - [-1][0]) / ([-2][1] - [-1][1]) >= ([-2][0] - p[0]) / ([-2][1] - p[1]) for (; qTail - qHead >= 2 && (q[qTail - 2][0] - q[qTail - 1][0]) * (q[qTail - 2][1] - p[1]) >= (q[qTail - 2][0] - p[0]) * (q[qTail - 2][1] - q[qTail - 1][1]); --qTail) {} q[qTail++] = p; } } writeln(ans); } } catch (EOFException e) { } }