import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.complex, std.container, std.math, 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(int M) { int x; this(ModInt a) { x = a.x; } this(long a) { x = cast(int)(a % M); if (x < 0) x += M; } ref ModInt opAssign(long a) { return (this = ModInt(a)); } ref ModInt opOpAssign(string op)(ModInt a) { static if (op == "+") { x += a.x; if (x >= M) x -= M; } else static if (op == "-") { x -= a.x; if (x < 0) x += M; } else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); } else static assert(false); return this; } ref ModInt opOpAssign(string op)(long a) { static if (op == "^^") { ModInt t2 = this, te = ModInt(1); for (long e = a; e; e >>= 1) { if (e & 1) te *= t2; t2 *= t2; } x = cast(int)(te.x); return this; } else return mixin("this " ~ op ~ "= ModInt(a)"); } ModInt inv() const { int a = x, b = M, y = 1, z = 0, t; for (; ; ) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1); return ModInt(b * z); } y -= t * z; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1); return ModInt(a * y); } z -= t * y; } } ModInt opUnary(string op)() const if (op == "-") { return ModInt(-x); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op)(long a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } string toString() const { return x.to!string; } } enum MO = 10L^^9 + 7; alias Mint = ModInt!MO; Mint eval(Mint[] f, Mint x) { Mint y; foreach_reverse (a; f) { y = y * x + a; } return y; } enum LIM = 1010; void main() { auto inv = new Mint[LIM]; inv[1] = 1; foreach (i; 2 .. LIM) { inv[i] = -Mint(MO / i) * inv[cast(size_t)(MO % i)]; } Mint eval(Mint[] f, Mint x) { Mint y; foreach_reverse (a; f) { y = y * x + a; } return y; } try { for (; ; ) { const N = readInt(); auto A = new long[N]; auto B = new long[N]; foreach (i; 0 .. N) { A[i] = readLong(); B[i] = readLong(); } auto xs = A.dup ~ B.dup; xs = xs.sort.uniq.array; const len = cast(int)(xs.length) - 1; auto dp = new Mint[][][](N, len, N); { const coef = Mint(B[0] - A[0]).inv; foreach (e; 0 .. len) { if (A[0] <= xs[e] && xs[e + 1] <= B[0]) { dp[0][e][0] = coef; } } } foreach (i; 1 .. N) { const coef = Mint(B[i] - A[i]).inv; if (i % 2 == 0) { // >= Mint sum; foreach_reverse (e; 0 .. len) { auto g = new Mint[i + 1]; foreach (d; 0 .. i) { g[d + 1] = dp[i - 1][e][d] * inv[d + 1]; } const y0 = g.eval(Mint(xs[e])); const y1 = g.eval(Mint(xs[e + 1])); if (A[i] <= xs[e] && xs[e + 1] <= B[i]) { foreach (d; 0 .. i) { dp[i][e][d + 1] = -g[d + 1]; } dp[i][e][0] += sum + y1; dp[i][e][] *= coef; } sum += y1 - y0; } } else { // <= Mint sum; foreach (e; 0 .. len) { auto g = new Mint[i + 1]; foreach (d; 0 .. i) { g[d + 1] = dp[i - 1][e][d] * inv[d + 1]; } const y0 = g.eval(Mint(xs[e])); const y1 = g.eval(Mint(xs[e + 1])); if (A[i] <= xs[e] && xs[e + 1] <= B[i]) { foreach (d; 0 .. i) { dp[i][e][d + 1] = g[d + 1]; } dp[i][e][0] += sum - y0; dp[i][e][] *= coef; } sum += y1 - y0; } } } debug { writeln("xs = ", xs); foreach (i; 0 .. N) { foreach (e; 0 .. len) { write(dp[i][e][0 .. i + 1], " "); } writeln(); } } Mint ans; foreach (e; 0 .. len) { auto g = new Mint[N + 1]; foreach (d; 0 .. N) { g[d + 1] = dp[N - 1][e][d] * inv[d + 1]; } const y0 = g.eval(Mint(xs[e])); const y1 = g.eval(Mint(xs[e + 1])); ans += y1 - y0; } writeln(ans); } } catch (EOFException e) { } }