#include #include #include #include using std::cin; using std::cout; const char endl = '\n'; const int N = 2e5 + 5, M = 2005; const int mod = 1e9 + 7; int n, m, a[N], b[N], inv[M << 2], fac[M << 2], inv_fac[M << 2], _f[M << 1][M << 1], *_pf[M << 1], **f, ans; inline int C(int n, int m) { return static_cast(fac[n]) * inv_fac[m] % mod * inv_fac[n - m] % mod; } int main() { std::ios::sync_with_stdio(false); cin.tie(nullptr); fac[0] = 1; for (int i = 1; i < M << 2; i++) { fac[i] = static_cast(fac[i - 1]) * i % mod; } inv[0] = inv[1] = 1; for (int i = 2; i < M << 2; i++) { inv[i] = static_cast(mod - (mod / i)) * inv[mod % i] % mod; } inv_fac[0] = inv_fac[1] = 1; for (int i = 2; i < M << 2; i++) { inv_fac[i] = static_cast(inv_fac[i - 1]) * inv[i] % mod; } for (int i = 0; i < M << 1; i++) { _pf[i] = _f[i] + M; } f = _pf + M; cin >> n; for (int i = 1; i <= n; i++) { cin >> a[i] >> b[i]; f[-a[i]][-b[i]]++; } for (int i = -2000; i <= 2000; i++) { for (int j = -2000; j <= 2000; j++) { f[i][j] = (static_cast(f[i][j]) + f[i - 1][j] + f[i][j - 1]) % mod; } } for (int i = 1; i <= n; i++) { ans = (static_cast(ans) + f[a[i]][b[i]]) % mod; } for (int i = 1; i <= n; i++) { ans = ((static_cast(ans) - C(2 * a[i] + 2 * b[i], 2 * a[i])) % mod + mod) % mod; } cout << (static_cast(ans) * inv[2] % mod) << endl; return 0; }