BigNumber = function (n, p, r) {
var o = this,
i;
if (n instanceof BigNumber) {
for (i in { precision: 0, roundType: 0, _s: 0, _f: 0 }) o = n;
o._d = n._d.slice();
return;
}
o.precision = isNaN((p = Math.abs(p))) ? BigNumber.defaultPrecision : p;
o.roundType = isNaN((r = Math.abs(r))) ? BigNumber.defaultRoundType : r;
o._s = (n += "").charAt(0) == "-";
o._f = ((n = n.replace(/[^\d.]/g, "").split(".", 2))[0] = n[0].replace(/^0+/, "") || "0").length;
for (i = (n = o._d = (n.join("") || "0").split("")).length; i; n[--i] = +n);
o.round();
};
with ({ $: BigNumber, o: BigNumber.prototype }) {
$.ROUND_HALF_EVEN = ($.ROUND_HALF_DOWN = ($.ROUND_HALF_UP = ($.ROUND_FLOOR = ($.ROUND_CEIL = ($.ROUND_DOWN = ($.ROUND_UP = 0) + 1) + 1) + 1) + 1) + 1) + 1;
$.defaultPrecision = 40;
$.defaultRoundType = $.ROUND_HALF_UP;
o.add = function (n) {
if (this._s != (n = new BigNumber(n))._s) return (n._s ^= 1), this.subtract(n);
var o = new BigNumber(this),
a = o._d,
b = n._d,
la = o._f,
lb = n._f,
n = Math.max(la, lb),
i,
r;
la != lb && ((lb = la - lb) > 0 ? o._zeroes(b, lb, 1) : o._zeroes(a, -lb, 1));
i = (la = a.length) == (lb = b.length) ? a.length : ((lb = la - lb) > 0 ? o._zeroes(b, lb) : o._zeroes(a, -lb)).length;
for (r = 0; i; r = ((a[--i] = a + b + r) / 10) >>> 0, a %= 10);
return r && ++n && a.unshift(r), (o._f = n), o.round();
};
o.subtract = function (n) {
if (this._s != (n = new BigNumber(n))._s) return (n._s ^= 1), this.add(n);
var o = new BigNumber(this),
c = o.abs().compare(n.abs()) + 1,
a = c ? o : n,
b = c ? n : o,
la = a._f,
lb = b._f,
d = la,
i,
j;
(a = a._d), (b = b._d), la != lb && ((lb = la - lb) > 0 ? o._zeroes(b, lb, 1) : o._zeroes(a, -lb, 1));
for (i = (la = a.length) == (lb = b.length) ? a.length : ((lb = la - lb) > 0 ? o._zeroes(b, lb) : o._zeroes(a, -lb)).length; i; ) {
if (a[--i] < b) {
for (j = i; j && !a[--j]; a[j] = 9);
--a[j], (a += 10);
}
b = a - b;
}
return c || (o._s ^= 1), (o._f = d), (o._d = b), o.round();
};
o.multiply = function (n) {
var o = new BigNumber(this),
r = o._d.length >= (n = new BigNumber(n))._d.length,
a = (r ? o : n)._d,
b = (r ? n : o)._d,
la = a.length,
lb = b.length,
x = new BigNumber(),
i,
j,
s;
for (i = lb; i; r && s.unshift(r), x.set(x.add(new BigNumber(s.join("")))))
for (s = new Array(lb - --i).join("0").split(""), r = 0, j = la; j; r += a[--j] * b, s.unshift(r % 10), r = (r / 10) >>> 0);
return (
(o._s = o._s != n._s),
(o._f = ((r = la + lb - o._f - n._f) >= (j = (o._d = x._d).length) ? this._zeroes(o._d, r - j + 1, 1).length : j) - r),
o.round()
);
};
o.divide = function (n) {
if ((n = new BigNumber(n)) == "0") throw new Error("Division by 0");
else if (this == "0") return new BigNumber();
var o = new BigNumber(this),
a = o._d,
b = n._d,
la = a.length - o._f,
lb = b.length - n._f,
r = new BigNumber(),
i = 0,
j,
s,
l,
f = 1,
c = 0,
e = 0;
(r._s = o._s != n._s),
(r.precision = Math.max(o.precision, n.precision)),
(r._f = +r._d.pop()),
la != lb && o._zeroes(la > lb ? b : a, Math.abs(la - lb));
(n._f = b.length), (b = n), (b._s = false), (b = b.round());
for (n = new BigNumber(); a[0] == "0"; a.shift());
out: do {
for (l = c = 0, n == "0" && ((n._d = []), (n._f = 0)); i < a.length && n.compare(b) == -1; ++i) {
((l = i + 1 == a.length), (!f && ++c > 1) || (e = l && n == "0" && a == "0")) && (r._f == r._d.length && ++r._f, r._d.push(0));
(a == "0" && n == "0") || (n._d.push(a), ++n._f);
if (e) break out;
if ((l && n.compare(b) == -1 && (r._f == r._d.length && ++r._f, 1)) || (l = 0))
while ((r._d.push(0), n._d.push(0), ++n._f, n.compare(b) == -1));
}
if (((f = 0), n.compare(b) == -1 && !(l = 0))) while ((l ? r._d.push(0) : (l = 1), n._d.push(0), ++n._f, n.compare(b) == -1));
for (s = new BigNumber(), j = 0; n.compare((y = s.add(b))) + 1 && ++j; s.set(y));
n.set(n.subtract(s)), !l && r._f == r._d.length && ++r._f, r._d.push(j);
} while ((i < a.length || n != "0") && r._d.length - r._f <= r.precision);
return r.round();
};
o.mod = function (n) {
return this.subtract(this.divide(n).intPart().multiply(n));
};
o.pow = function (n) {
var o = new BigNumber(this),
i;
if ((n = new BigNumber(n).intPart()) == 0) return o.set(1);
for (i = Math.abs(n); --i; o.set(o.multiply(this)));
return n < 0 ? o.set(new BigNumber(1).divide(o)) : o;
};
o.set = function (n) {
return this.constructor(n), this;
};
o.compare = function (n) {
var a = this,
la = this._f,
b = new BigNumber(n),
lb = b._f,
r = [-1, 1],
i,
l;
if (a._s != b._s) return a._s ? -1 : 1;
if (la != lb) return r[(la > lb) ^ a._s];
for (la = (a = a._d).length, lb = (b = b._d).length, i = -1, l = Math.min(la, lb); ++i < l; ) if (a != b) return r[(a > b) ^ a._s];
return la != lb ? r[(la > lb) ^ a._s] : 0;
};
o.negate = function () {
var n = new BigNumber(this);
return (n._s ^= 1), n;
};
o.abs = function () {
var n = new BigNumber(this);
return (n._s = 0), n;
};
o.intPart = function () {
return new BigNumber((this._s ? "-" : "") + (this._d.slice(0, this._f).join("") || "0"));
};
o.valueOf = o.toString = function () {
var o = this;
return (o._s ? "-" : "") + (o._d.slice(0, o._f).join("") || "0") + (o._f != o._d.length ? "." + o._d.slice(o._f).join("") : "");
};
o._zeroes = function (n, l, t) {
var s = ["push", "unshift"][t || 0];
for (++l; --l; n(0));
return n;
};
o.round = function () {
if ("_rounding" in this) return this;
var $ = BigNumber,
r = this.roundType,
b = this._d,
d,
p,
n,
x;
for (this._rounding = true; this._f > 1 && !b[0]; --this._f, b.shift());
for (d = this._f, p = this.precision + d, n = b[p]; b.length > d && !b[b.length - 1]; b.pop());
x = (this._s ? "-" : "") + (p - d ? "0." + this._zeroes([], p - d - 1).join("") : "") + 1;
if (b.length > p) {
n &&
(r == $.DOWN
? false
: r == $.UP
? true
: r == $.CEIL
? !this._s
: r == $.FLOOR
? this._s
: r == $.HALF_UP
? n >= 5
: r == $.HALF_DOWN
? n > 5
: r == $.HALF_EVEN
? n >= 5 && b[p - 1] & 1
: false) &&
this.add(x);
b.splice(p, b.length - p);
}
return delete this._rounding, this;
};
}
function sumStrings(a, b) {
if (a === "") {
a = "0";
} else if (b === "") {
b = "0";
}
var result = new BigNumber(a).add(b);
return result.toString();
}
sumStrings("712569312664357328695151392", "8100824045303269669937");