"use strict";
var bigInt = function (undefined) { "use strict"; var BASE = 1e7, LOG_BASE = 7, MAX_INT = 9007199254740992, MAX_INT_ARR = smallToArray(MAX_INT), LOG_MAX_INT = Math.log(MAX_INT); function Integer(v, radix) { if (typeof v === "undefined") return Integer[0]; if (typeof radix !== "undefined") return +radix === 10 ? parseValue(v) : parseBase(v, radix); return parseValue(v) } function BigInteger(value, sign) { this.value = value; this.sign = sign; this.isSmall = false } BigInteger.prototype = Object.create(Integer.prototype); function SmallInteger(value) { this.value = value; this.sign = value < 0; this.isSmall = true } SmallInteger.prototype = Object.create(Integer.prototype); function isPrecise(n) { return -MAX_INT < n && n < MAX_INT } function smallToArray(n) { if (n < 1e7) return [n]; if (n < 1e14) return [n % 1e7, Math.floor(n / 1e7)]; return [n % 1e7, Math.floor(n / 1e7) % 1e7, Math.floor(n / 1e14)] } function arrayToSmall(arr) { trim(arr); var length = arr.length; if (length < 4 && compareAbs(arr, MAX_INT_ARR) < 0) { switch (length) { case 0: return 0; case 1: return arr[0]; case 2: return arr[0] + arr[1] * BASE; default: return arr[0] + (arr[1] + arr[2] * BASE) * BASE } } return arr } function trim(v) { var i = v.length; while (v[--i] === 0); v.length = i + 1 } function createArray(length) { var x = new Array(length); var i = -1; while (++i < length) { x[i] = 0 } return x } function truncate(n) { if (n > 0) return Math.floor(n); return Math.ceil(n) } function add(a, b) { var l_a = a.length, l_b = b.length, r = new Array(l_a), carry = 0, base = BASE, sum, i; for (i = 0; i < l_b; i++) { sum = a[i] + b[i] + carry; carry = sum >= base ? 1 : 0; r[i] = sum - carry * base } while (i < l_a) { sum = a[i] + carry; carry = sum === base ? 1 : 0; r[i++] = sum - carry * base } if (carry > 0) r.push(carry); return r } function addAny(a, b) { if (a.length >= b.length) return add(a, b); return add(b, a) } function addSmall(a, carry) { var l = a.length, r = new Array(l), base = BASE, sum, i; for (i = 0; i < l; i++) { sum = a[i] - base + carry; carry = Math.floor(sum / base); r[i] = sum - carry * base; carry += 1 } while (carry > 0) { r[i++] = carry % base; carry = Math.floor(carry / base) } return r } BigInteger.prototype.add = function (v) { var n = parseValue(v); if (this.sign !== n.sign) { return this.subtract(n.negate()) } var a = this.value, b = n.value; if (n.isSmall) { return new BigInteger(addSmall(a, Math.abs(b)), this.sign) } return new BigInteger(addAny(a, b), this.sign) }; BigInteger.prototype.plus = BigInteger.prototype.add; SmallInteger.prototype.add = function (v) { var n = parseValue(v); var a = this.value; if (a < 0 !== n.sign) { return this.subtract(n.negate()) } var b = n.value; if (n.isSmall) { if (isPrecise(a + b)) return new SmallInteger(a + b); b = smallToArray(Math.abs(b)) } return new BigInteger(addSmall(b, Math.abs(a)), a < 0) }; SmallInteger.prototype.plus = SmallInteger.prototype.add; function subtract(a, b) { var a_l = a.length, b_l = b.length, r = new Array(a_l), borrow = 0, base = BASE, i, difference; for (i = 0; i < b_l; i++) { difference = a[i] - borrow - b[i]; if (difference < 0) { difference += base; borrow = 1 } else borrow = 0; r[i] = difference } for (i = b_l; i < a_l; i++) { difference = a[i] - borrow; if (difference < 0) difference += base; else { r[i++] = difference; break } r[i] = difference } for (; i < a_l; i++) { r[i] = a[i] } trim(r); return r } function subtractAny(a, b, sign) { var value; if (compareAbs(a, b) >= 0) { value = subtract(a, b) } else { value = subtract(b, a); sign = !sign } value = arrayToSmall(value); if (typeof value === "number") { if (sign) value = -value; return new SmallInteger(value) } return new BigInteger(value, sign) } function subtractSmall(a, b, sign) { var l = a.length, r = new Array(l), carry = -b, base = BASE, i, difference; for (i = 0; i < l; i++) { difference = a[i] + carry; carry = Math.floor(difference / base); difference %= base; r[i] = difference < 0 ? difference + base : difference } r = arrayToSmall(r); if (typeof r === "number") { if (sign) r = -r; return new SmallInteger(r) } return new BigInteger(r, sign) } BigInteger.prototype.subtract = function (v) { var n = parseValue(v); if (this.sign !== n.sign) { return this.add(n.negate()) } var a = this.value, b = n.value; if (n.isSmall) return subtractSmall(a, Math.abs(b), this.sign); return subtractAny(a, b, this.sign) }; BigInteger.prototype.minus = BigInteger.prototype.subtract; SmallInteger.prototype.subtract = function (v) { var n = parseValue(v); var a = this.value; if (a < 0 !== n.sign) { return this.add(n.negate()) } var b = n.value; if (n.isSmall) { return new SmallInteger(a - b) } return subtractSmall(b, Math.abs(a), a >= 0) }; SmallInteger.prototype.minus = SmallInteger.prototype.subtract; BigInteger.prototype.negate = function () { return new BigInteger(this.value, !this.sign) }; SmallInteger.prototype.negate = function () { var sign = this.sign; var small = new SmallInteger(-this.value); small.sign = !sign; return small }; BigInteger.prototype.abs = function () { return new BigInteger(this.value, false) }; SmallInteger.prototype.abs = function () { return new SmallInteger(Math.abs(this.value)) }; function multiplyLong(a, b) { var a_l = a.length, b_l = b.length, l = a_l + b_l, r = createArray(l), base = BASE, product, carry, i, a_i, b_j; for (i = 0; i < a_l; ++i) { a_i = a[i]; for (var j = 0; j < b_l; ++j) { b_j = b[j]; product = a_i * b_j + r[i + j]; carry = Math.floor(product / base); r[i + j] = product - carry * base; r[i + j + 1] += carry } } trim(r); return r } function multiplySmall(a, b) { var l = a.length, r = new Array(l), base = BASE, carry = 0, product, i; for (i = 0; i < l; i++) { product = a[i] * b + carry; carry = Math.floor(product / base); r[i] = product - carry * base } while (carry > 0) { r[i++] = carry % base; carry = Math.floor(carry / base) } return r } function shiftLeft(x, n) { var r = []; while (n-- > 0) r.push(0); return r.concat(x) } function multiplyKaratsuba(x, y) { var n = Math.max(x.length, y.length); if (n <= 30) return multiplyLong(x, y); n = Math.ceil(n / 2); var b = x.slice(n), a = x.slice(0, n), d = y.slice(n), c = y.slice(0, n); var ac = multiplyKaratsuba(a, c), bd = multiplyKaratsuba(b, d), abcd = multiplyKaratsuba(addAny(a, b), addAny(c, d)); var product = addAny(addAny(ac, shiftLeft(subtract(subtract(abcd, ac), bd), n)), shiftLeft(bd, 2 * n)); trim(product); return product } function useKaratsuba(l1, l2) { return -.012 * l1 - .012 * l2 + 15e-6 * l1 * l2 > 0 } BigInteger.prototype.multiply = function (v) { var n = parseValue(v), a = this.value, b = n.value, sign = this.sign !== n.sign, abs; if (n.isSmall) { if (b === 0) return Integer[0]; if (b === 1) return this; if (b === -1) return this.negate(); abs = Math.abs(b); if (abs < BASE) { return new BigInteger(multiplySmall(a, abs), sign) } b = smallToArray(abs) } if (useKaratsuba(a.length, b.length)) return new BigInteger(multiplyKaratsuba(a, b), sign); return new BigInteger(multiplyLong(a, b), sign) }; BigInteger.prototype.times = BigInteger.prototype.multiply; function multiplySmallAndArray(a, b, sign) { if (a < BASE) { return new BigInteger(multiplySmall(b, a), sign) } return new BigInteger(multiplyLong(b, smallToArray(a)), sign) } SmallInteger.prototype._multiplyBySmall = function (a) { if (isPrecise(a.value * this.value)) { return new SmallInteger(a.value * this.value) } return multiplySmallAndArray(Math.abs(a.value), smallToArray(Math.abs(this.value)), this.sign !== a.sign) }; BigInteger.prototype._multiplyBySmall = function (a) { if (a.value === 0) return Integer[0]; if (a.value === 1) return this; if (a.value === -1) return this.negate(); return multiplySmallAndArray(Math.abs(a.value), this.value, this.sign !== a.sign) }; SmallInteger.prototype.multiply = function (v) { return parseValue(v)._multiplyBySmall(this) }; SmallInteger.prototype.times = SmallInteger.prototype.multiply; function square(a) { var l = a.length, r = createArray(l + l), base = BASE, product, carry, i, a_i, a_j; for (i = 0; i < l; i++) { a_i = a[i]; carry = 0 - a_i * a_i; for (var j = i; j < l; j++) { a_j = a[j]; product = 2 * (a_i * a_j) + r[i + j] + carry; carry = Math.floor(product / base); r[i + j] = product - carry * base } r[i + l] = carry } trim(r); return r } BigInteger.prototype.square = function () { return new BigInteger(square(this.value), false) }; SmallInteger.prototype.square = function () { var value = this.value * this.value; if (isPrecise(value)) return new SmallInteger(value); return new BigInteger(square(smallToArray(Math.abs(this.value))), false) }; function divMod1(a, b) { var a_l = a.length, b_l = b.length, base = BASE, result = createArray(b.length), divisorMostSignificantDigit = b[b_l - 1], lambda = Math.ceil(base / (2 * divisorMostSignificantDigit)), remainder = multiplySmall(a, lambda), divisor = multiplySmall(b, lambda), quotientDigit, shift, carry, borrow, i, l, q; if (remainder.length <= a_l) remainder.push(0); divisor.push(0); divisorMostSignificantDigit = divisor[b_l - 1]; for (shift = a_l - b_l; shift >= 0; shift--) { quotientDigit = base - 1; if (remainder[shift + b_l] !== divisorMostSignificantDigit) { quotientDigit = Math.floor((remainder[shift + b_l] * base + remainder[shift + b_l - 1]) / divisorMostSignificantDigit) } carry = 0; borrow = 0; l = divisor.length; for (i = 0; i < l; i++) { carry += quotientDigit * divisor[i]; q = Math.floor(carry / base); borrow += remainder[shift + i] - (carry - q * base); carry = q; if (borrow < 0) { remainder[shift + i] = borrow + base; borrow = -1 } else { remainder[shift + i] = borrow; borrow = 0 } } while (borrow !== 0) { quotientDigit -= 1; carry = 0; for (i = 0; i < l; i++) { carry += remainder[shift + i] - base + divisor[i]; if (carry < 0) { remainder[shift + i] = carry + base; carry = 0 } else { remainder[shift + i] = carry; carry = 1 } } borrow += carry } result[shift] = quotientDigit } remainder = divModSmall(remainder, lambda)[0]; return [arrayToSmall(result), arrayToSmall(remainder)] } function divMod2(a, b) { var a_l = a.length, b_l = b.length, result = [], part = [], base = BASE, guess, xlen, highx, highy, check; while (a_l) { part.unshift(a[--a_l]); trim(part); if (compareAbs(part, b) < 0) { result.push(0); continue } xlen = part.length; highx = part[xlen - 1] * base + part[xlen - 2]; highy = b[b_l - 1] * base + b[b_l - 2]; if (xlen > b_l) { highx = (highx + 1) * base } guess = Math.ceil(highx / highy); do { check = multiplySmall(b, guess); if (compareAbs(check, part) <= 0) break; guess-- } while (guess); result.push(guess); part = subtract(part, check) } result.reverse(); return [arrayToSmall(result), arrayToSmall(part)] } function divModSmall(value, lambda) { var length = value.length, quotient = createArray(length), base = BASE, i, q, remainder, divisor; remainder = 0; for (i = length - 1; i >= 0; --i) { divisor = remainder * base + value[i]; q = truncate(divisor / lambda); remainder = divisor - q * lambda; quotient[i] = q | 0 } return [quotient, remainder | 0] } function divModAny(self, v) { var value, n = parseValue(v); var a = self.value, b = n.value; var quotient; if (b === 0) throw new Error("Cannot divide by zero"); if (self.isSmall) { if (n.isSmall) { return [new SmallInteger(truncate(a / b)), new SmallInteger(a % b)] } return [Integer[0], self] } if (n.isSmall) { if (b === 1) return [self, Integer[0]]; if (b == -1) return [self.negate(), Integer[0]]; var abs = Math.abs(b); if (abs < BASE) { value = divModSmall(a, abs); quotient = arrayToSmall(value[0]); var remainder = value[1]; if (self.sign) remainder = -remainder; if (typeof quotient === "number") { if (self.sign !== n.sign) quotient = -quotient; return [new SmallInteger(quotient), new SmallInteger(remainder)] } return [new BigInteger(quotient, self.sign !== n.sign), new SmallInteger(remainder)] } b = smallToArray(abs) } var comparison = compareAbs(a, b); if (comparison === -1) return [Integer[0], self]; if (comparison === 0) return [Integer[self.sign === n.sign ? 1 : -1], Integer[0]]; if (a.length + b.length <= 200) value = divMod1(a, b); else value = divMod2(a, b); quotient = value[0]; var qSign = self.sign !== n.sign, mod = value[1], mSign = self.sign; if (typeof quotient === "number") { if (qSign) quotient = -quotient; quotient = new SmallInteger(quotient) } else quotient = new BigInteger(quotient, qSign); if (typeof mod === "number") { if (mSign) mod = -mod; mod = new SmallInteger(mod) } else mod = new BigInteger(mod, mSign); return [quotient, mod] } BigInteger.prototype.divmod = function (v) { var result = divModAny(this, v); return { quotient: result[0], remainder: result[1] } }; SmallInteger.prototype.divmod = BigInteger.prototype.divmod; BigInteger.prototype.divide = function (v) { return divModAny(this, v)[0] }; SmallInteger.prototype.over = SmallInteger.prototype.divide = BigInteger.prototype.over = BigInteger.prototype.divide; BigInteger.prototype.mod = function (v) { return divModAny(this, v)[1] }; SmallInteger.prototype.remainder = SmallInteger.prototype.mod = BigInteger.prototype.remainder = BigInteger.prototype.mod; BigInteger.prototype.pow = function (v) { var n = parseValue(v), a = this.value, b = n.value, value, x, y; if (b === 0) return Integer[1]; if (a === 0) return Integer[0]; if (a === 1) return Integer[1]; if (a === -1) return n.isEven() ? Integer[1] : Integer[-1]; if (n.sign) { return Integer[0] } if (!n.isSmall) throw new Error("The exponent " + n.toString() + " is too large."); if (this.isSmall) { if (isPrecise(value = Math.pow(a, b))) return new SmallInteger(truncate(value)) } x = this; y = Integer[1]; while (true) { if (b & 1 === 1) { y = y.times(x); --b } if (b === 0) break; b /= 2; x = x.square() } return y }; SmallInteger.prototype.pow = BigInteger.prototype.pow; BigInteger.prototype.modPow = function (exp, mod) { exp = parseValue(exp); mod = parseValue(mod); if (mod.isZero()) throw new Error("Cannot take modPow with modulus 0"); var r = Integer[1], base = this.mod(mod); while (exp.isPositive()) { if (base.isZero()) return Integer[0]; if (exp.isOdd()) r = r.multiply(base).mod(mod); exp = exp.divide(2); base = base.square().mod(mod) } return r }; SmallInteger.prototype.modPow = BigInteger.prototype.modPow; function compareAbs(a, b) { if (a.length !== b.length) { return a.length > b.length ? 1 : -1 } for (var i = a.length - 1; i >= 0; i--) { if (a[i] !== b[i]) return a[i] > b[i] ? 1 : -1 } return 0 } BigInteger.prototype.compareAbs = function (v) { var n = parseValue(v), a = this.value, b = n.value; if (n.isSmall) return 1; return compareAbs(a, b) }; SmallInteger.prototype.compareAbs = function (v) { var n = parseValue(v), a = Math.abs(this.value), b = n.value; if (n.isSmall) { b = Math.abs(b); return a === b ? 0 : a > b ? 1 : -1 } return -1 }; BigInteger.prototype.compare = function (v) { if (v === Infinity) { return -1 } if (v === -Infinity) { return 1 } var n = parseValue(v), a = this.value, b = n.value; if (this.sign !== n.sign) { return n.sign ? 1 : -1 } if (n.isSmall) { return this.sign ? -1 : 1 } return compareAbs(a, b) * (this.sign ? -1 : 1) }; BigInteger.prototype.compareTo = BigInteger.prototype.compare; SmallInteger.prototype.compare = function (v) { if (v === Infinity) { return -1 } if (v === -Infinity) { return 1 } var n = parseValue(v), a = this.value, b = n.value; if (n.isSmall) { return a == b ? 0 : a > b ? 1 : -1 } if (a < 0 !== n.sign) { return a < 0 ? -1 : 1 } return a < 0 ? 1 : -1 }; SmallInteger.prototype.compareTo = SmallInteger.prototype.compare; BigInteger.prototype.equals = function (v) { return this.compare(v) === 0 }; SmallInteger.prototype.eq = SmallInteger.prototype.equals = BigInteger.prototype.eq = BigInteger.prototype.equals; BigInteger.prototype.notEquals = function (v) { return this.compare(v) !== 0 }; SmallInteger.prototype.neq = SmallInteger.prototype.notEquals = BigInteger.prototype.neq = BigInteger.prototype.notEquals; BigInteger.prototype.greater = function (v) { return this.compare(v) > 0 }; SmallInteger.prototype.gt = SmallInteger.prototype.greater = BigInteger.prototype.gt = BigInteger.prototype.greater; BigInteger.prototype.lesser = function (v) { return this.compare(v) < 0 }; SmallInteger.prototype.lt = SmallInteger.prototype.lesser = BigInteger.prototype.lt = BigInteger.prototype.lesser; BigInteger.prototype.greaterOrEquals = function (v) { return this.compare(v) >= 0 }; SmallInteger.prototype.geq = SmallInteger.prototype.greaterOrEquals = BigInteger.prototype.geq = BigInteger.prototype.greaterOrEquals; BigInteger.prototype.lesserOrEquals = function (v) { return this.compare(v) <= 0 }; SmallInteger.prototype.leq = SmallInteger.prototype.lesserOrEquals = BigInteger.prototype.leq = BigInteger.prototype.lesserOrEquals; BigInteger.prototype.isEven = function () { return (this.value[0] & 1) === 0 }; SmallInteger.prototype.isEven = function () { return (this.value & 1) === 0 }; BigInteger.prototype.isOdd = function () { return (this.value[0] & 1) === 1 }; SmallInteger.prototype.isOdd = function () { return (this.value & 1) === 1 }; BigInteger.prototype.isPositive = function () { return !this.sign }; SmallInteger.prototype.isPositive = function () { return this.value > 0 }; BigInteger.prototype.isNegative = function () { return this.sign }; SmallInteger.prototype.isNegative = function () { return this.value < 0 }; BigInteger.prototype.isUnit = function () { return false }; SmallInteger.prototype.isUnit = function () { return Math.abs(this.value) === 1 }; BigInteger.prototype.isZero = function () { return false }; SmallInteger.prototype.isZero = function () { return this.value === 0 }; BigInteger.prototype.isDivisibleBy = function (v) { var n = parseValue(v); var value = n.value; if (value === 0) return false; if (value === 1) return true; if (value === 2) return this.isEven(); return this.mod(n).equals(Integer[0]) }; SmallInteger.prototype.isDivisibleBy = BigInteger.prototype.isDivisibleBy; function isBasicPrime(v) { var n = v.abs(); if (n.isUnit()) return false; if (n.equals(2) || n.equals(3) || n.equals(5)) return true; if (n.isEven() || n.isDivisibleBy(3) || n.isDivisibleBy(5)) return false; if (n.lesser(25)) return true } BigInteger.prototype.isPrime = function () { var isPrime = isBasicPrime(this); if (isPrime !== undefined) return isPrime; var n = this.abs(), nPrev = n.prev(); var a = [2, 3, 5, 7, 11, 13, 17, 19], b = nPrev, d, t, i, x; while (b.isEven()) b = b.divide(2); for (i = 0; i < a.length; i++) { x = bigInt(a[i]).modPow(b, n); if (x.equals(Integer[1]) || x.equals(nPrev)) continue; for (t = true, d = b; t && d.lesser(nPrev); d = d.multiply(2)) { x = x.square().mod(n); if (x.equals(nPrev)) t = false } if (t) return false } return true }; SmallInteger.prototype.isPrime = BigInteger.prototype.isPrime; BigInteger.prototype.isProbablePrime = function (iterations) { var isPrime = isBasicPrime(this); if (isPrime !== undefined) return isPrime; var n = this.abs(); var t = iterations === undefined ? 5 : iterations; for (var i = 0; i < t; i++) { var a = bigInt.randBetween(2, n.minus(2)); if (!a.modPow(n.prev(), n).isUnit()) return false } return true }; SmallInteger.prototype.isProbablePrime = BigInteger.prototype.isProbablePrime; BigInteger.prototype.modInv = function (n) { var t = bigInt.zero, newT = bigInt.one, r = parseValue(n), newR = this.abs(), q, lastT, lastR; while (!newR.equals(bigInt.zero)) { q = r.divide(newR); lastT = t; lastR = r; t = newT; r = newR; newT = lastT.subtract(q.multiply(newT)); newR = lastR.subtract(q.multiply(newR)) } if (!r.equals(1)) throw new Error(this.toString() + " and " + n.toString() + " are not co-prime"); if (t.compare(0) === -1) { t = t.add(n) } if (this.isNegative()) { return t.negate() } return t }; SmallInteger.prototype.modInv = BigInteger.prototype.modInv; BigInteger.prototype.next = function () { var value = this.value; if (this.sign) { return subtractSmall(value, 1, this.sign) } return new BigInteger(addSmall(value, 1), this.sign) }; SmallInteger.prototype.next = function () { var value = this.value; if (value + 1 < MAX_INT) return new SmallInteger(value + 1); return new BigInteger(MAX_INT_ARR, false) }; BigInteger.prototype.prev = function () { var value = this.value; if (this.sign) { return new BigInteger(addSmall(value, 1), true) } return subtractSmall(value, 1, this.sign) }; SmallInteger.prototype.prev = function () { var value = this.value; if (value - 1 > -MAX_INT) return new SmallInteger(value - 1); return new BigInteger(MAX_INT_ARR, true) }; var powersOfTwo = [1]; while (2 * powersOfTwo[powersOfTwo.length - 1] <= BASE) powersOfTwo.push(2 * powersOfTwo[powersOfTwo.length - 1]); var powers2Length = powersOfTwo.length, highestPower2 = powersOfTwo[powers2Length - 1]; function shift_isSmall(n) { return (typeof n === "number" || typeof n === "string") && +Math.abs(n) <= BASE || n instanceof BigInteger && n.value.length <= 1 } BigInteger.prototype.shiftLeft = function (n) { if (!shift_isSmall(n)) { throw new Error(String(n) + " is too large for shifting.") } n = +n; if (n < 0) return this.shiftRight(-n); var result = this; if (result.isZero()) return result; while (n >= powers2Length) { result = result.multiply(highestPower2); n -= powers2Length - 1 } return result.multiply(powersOfTwo[n]) }; SmallInteger.prototype.shiftLeft = BigInteger.prototype.shiftLeft; BigInteger.prototype.shiftRight = function (n) { var remQuo; if (!shift_isSmall(n)) { throw new Error(String(n) + " is too large for shifting.") } n = +n; if (n < 0) return this.shiftLeft(-n); var result = this; while (n >= powers2Length) { if (result.isZero() || result.isNegative() && result.isUnit()) return result; remQuo = divModAny(result, highestPower2); result = remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0]; n -= powers2Length - 1 } remQuo = divModAny(result, powersOfTwo[n]); return remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0] }; SmallInteger.prototype.shiftRight = BigInteger.prototype.shiftRight; function bitwise(x, y, fn) { y = parseValue(y); var xSign = x.isNegative(), ySign = y.isNegative(); var xRem = xSign ? x.not() : x, yRem = ySign ? y.not() : y; var xDigit = 0, yDigit = 0; var xDivMod = null, yDivMod = null; var result = []; while (!xRem.isZero() || !yRem.isZero()) { xDivMod = divModAny(xRem, highestPower2); xDigit = xDivMod[1].toJSNumber(); if (xSign) { xDigit = highestPower2 - 1 - xDigit } yDivMod = divModAny(yRem, highestPower2); yDigit = yDivMod[1].toJSNumber(); if (ySign) { yDigit = highestPower2 - 1 - yDigit } xRem = xDivMod[0]; yRem = yDivMod[0]; result.push(fn(xDigit, yDigit)) } var sum = fn(xSign ? 1 : 0, ySign ? 1 : 0) !== 0 ? bigInt(-1) : bigInt(0); for (var i = result.length - 1; i >= 0; i -= 1) { sum = sum.multiply(highestPower2).add(bigInt(result[i])) } return sum } BigInteger.prototype.not = function () { return this.negate().prev() }; SmallInteger.prototype.not = BigInteger.prototype.not; BigInteger.prototype.and = function (n) { return bitwise(this, n, function (a, b) { return a & b }) }; SmallInteger.prototype.and = BigInteger.prototype.and; BigInteger.prototype.or = function (n) { return bitwise(this, n, function (a, b) { return a | b }) }; SmallInteger.prototype.or = BigInteger.prototype.or; BigInteger.prototype.xor = function (n) { return bitwise(this, n, function (a, b) { return a ^ b }) }; SmallInteger.prototype.xor = BigInteger.prototype.xor; var LOBMASK_I = 1 << 30, LOBMASK_BI = (BASE & -BASE) * (BASE & -BASE) | LOBMASK_I; function roughLOB(n) { var v = n.value, x = typeof v === "number" ? v | LOBMASK_I : v[0] + v[1] * BASE | LOBMASK_BI; return x & -x } function integerLogarithm(value, base) { if (base.compareTo(value) <= 0) { var tmp = integerLogarithm(value, base.square(base)); var p = tmp.p; var e = tmp.e; var t = p.multiply(base); return t.compareTo(value) <= 0 ? { p: t, e: e * 2 + 1 } : { p: p, e: e * 2 } } return { p: bigInt(1), e: 0 } } BigInteger.prototype.bitLength = function () { var n = this; if (n.compareTo(bigInt(0)) < 0) { n = n.negate().subtract(bigInt(1)) } if (n.compareTo(bigInt(0)) === 0) { return bigInt(0) } return bigInt(integerLogarithm(n, bigInt(2)).e).add(bigInt(1)) }; SmallInteger.prototype.bitLength = BigInteger.prototype.bitLength; function max(a, b) { a = parseValue(a); b = parseValue(b); return a.greater(b) ? a : b } function min(a, b) { a = parseValue(a); b = parseValue(b); return a.lesser(b) ? a : b } function gcd(a, b) { a = parseValue(a).abs(); b = parseValue(b).abs(); if (a.equals(b)) return a; if (a.isZero()) return b; if (b.isZero()) return a; var c = Integer[1], d, t; while (a.isEven() && b.isEven()) { d = Math.min(roughLOB(a), roughLOB(b)); a = a.divide(d); b = b.divide(d); c = c.multiply(d) } while (a.isEven()) { a = a.divide(roughLOB(a)) } do { while (b.isEven()) { b = b.divide(roughLOB(b)) } if (a.greater(b)) { t = b; b = a; a = t } b = b.subtract(a) } while (!b.isZero()); return c.isUnit() ? a : a.multiply(c) } function lcm(a, b) { a = parseValue(a).abs(); b = parseValue(b).abs(); return a.divide(gcd(a, b)).multiply(b) } function randBetween(a, b) { a = parseValue(a); b = parseValue(b); var low = min(a, b), high = max(a, b); var range = high.subtract(low).add(1); if (range.isSmall) return low.add(Math.floor(Math.random() * range)); var length = range.value.length - 1; var result = [], restricted = true; for (var i = length; i >= 0; i--) { var top = restricted ? range.value[i] : BASE; var digit = truncate(Math.random() * top); result.unshift(digit); if (digit < top) restricted = false } result = arrayToSmall(result); return low.add(typeof result === "number" ? new SmallInteger(result) : new BigInteger(result, false)) } var parseBase = function (text, base) { var length = text.length; var i; var absBase = Math.abs(base); for (var i = 0; i < length; i++) { var c = text[i].toLowerCase(); if (c === "-") continue; if (/[a-z0-9]/.test(c)) { if (/[0-9]/.test(c) && +c >= absBase) { if (c === "1" && absBase === 1) continue; throw new Error(c + " is not a valid digit in base " + base + ".") } else if (c.charCodeAt(0) - 87 >= absBase) { throw new Error(c + " is not a valid digit in base " + base + ".") } } } if (2 <= base && base <= 36) { if (length <= LOG_MAX_INT / Math.log(base)) { var result = parseInt(text, base); if (isNaN(result)) { throw new Error(c + " is not a valid digit in base " + base + ".") } return new SmallInteger(parseInt(text, base)) } } base = parseValue(base); var digits = []; var isNegative = text[0] === "-"; for (i = isNegative ? 1 : 0; i < text.length; i++) { var c = text[i].toLowerCase(), charCode = c.charCodeAt(0); if (48 <= charCode && charCode <= 57) digits.push(parseValue(c)); else if (97 <= charCode && charCode <= 122) digits.push(parseValue(c.charCodeAt(0) - 87)); else if (c === "<") { var start = i; do { i++ } while (text[i] !== ">"); digits.push(parseValue(text.slice(start + 1, i))) } else throw new Error(c + " is not a valid character") } return parseBaseFromArray(digits, base, isNegative) }; function parseBaseFromArray(digits, base, isNegative) { var val = Integer[0], pow = Integer[1], i; for (i = digits.length - 1; i >= 0; i--) { val = val.add(digits[i].times(pow)); pow = pow.times(base) } return isNegative ? val.negate() : val } function stringify(digit) { if (digit <= 35) { return "0123456789abcdefghijklmnopqrstuvwxyz".charAt(digit) } return "<" + digit + ">" } function toBase(n, base) { base = bigInt(base); if (base.isZero()) { if (n.isZero()) return { value: [0], isNegative: false }; throw new Error("Cannot convert nonzero numbers to base 0.") } if (base.equals(-1)) { if (n.isZero()) return { value: [0], isNegative: false }; if (n.isNegative()) return { value: [].concat.apply([], Array.apply(null, Array(-n)).map(Array.prototype.valueOf, [1, 0])), isNegative: false }; var arr = Array.apply(null, Array(+n - 1)).map(Array.prototype.valueOf, [0, 1]); arr.unshift([1]); return { value: [].concat.apply([], arr), isNegative: false } } var neg = false; if (n.isNegative() && base.isPositive()) { neg = true; n = n.abs() } if (base.equals(1)) { if (n.isZero()) return { value: [0], isNegative: false }; return { value: Array.apply(null, Array(+n)).map(Number.prototype.valueOf, 1), isNegative: neg } } var out = []; var left = n, divmod; while (left.isNegative() || left.compareAbs(base) >= 0) { divmod = left.divmod(base); left = divmod.quotient; var digit = divmod.remainder; if (digit.isNegative()) { digit = base.minus(digit).abs(); left = left.next() } out.push(digit.toJSNumber()) } out.push(left.toJSNumber()); return { value: out.reverse(), isNegative: neg } } function toBaseString(n, base) { var arr = toBase(n, base); return (arr.isNegative ? "-" : "") + arr.value.map(stringify).join("") } BigInteger.prototype.toArray = function (radix) { return toBase(this, radix) }; SmallInteger.prototype.toArray = function (radix) { return toBase(this, radix) }; BigInteger.prototype.toString = function (radix) { if (radix === undefined) radix = 10; if (radix !== 10) return toBaseString(this, radix); var v = this.value, l = v.length, str = String(v[--l]), zeros = "0000000", digit; while (--l >= 0) { digit = String(v[l]); str += zeros.slice(digit.length) + digit } var sign = this.sign ? "-" : ""; return sign + str }; SmallInteger.prototype.toString = function (radix) { if (radix === undefined) radix = 10; if (radix != 10) return toBaseString(this, radix); return String(this.value) }; BigInteger.prototype.toJSON = SmallInteger.prototype.toJSON = function () { return this.toString() }; BigInteger.prototype.valueOf = function () { return parseInt(this.toString(), 10) }; BigInteger.prototype.toJSNumber = BigInteger.prototype.valueOf; SmallInteger.prototype.valueOf = function () { return this.value }; SmallInteger.prototype.toJSNumber = SmallInteger.prototype.valueOf; function parseStringValue(v) { if (isPrecise(+v)) { var x = +v; if (x === truncate(x)) return new SmallInteger(x); throw new Error("Invalid integer: " + v) } var sign = v[0] === "-"; if (sign) v = v.slice(1); var split = v.split(/e/i); if (split.length > 2) throw new Error("Invalid integer: " + split.join("e")); if (split.length === 2) { var exp = split[1]; if (exp[0] === "+") exp = exp.slice(1); exp = +exp; if (exp !== truncate(exp) || !isPrecise(exp)) throw new Error("Invalid integer: " + exp + " is not a valid exponent."); var text = split[0]; var decimalPlace = text.indexOf("."); if (decimalPlace >= 0) { exp -= text.length - decimalPlace - 1; text = text.slice(0, decimalPlace) + text.slice(decimalPlace + 1) } if (exp < 0) throw new Error("Cannot include negative exponent part for integers"); text += new Array(exp + 1).join("0"); v = text } var isValid = /^([0-9][0-9]*)$/.test(v); if (!isValid) throw new Error("Invalid integer: " + v); var r = [], max = v.length, l = LOG_BASE, min = max - l; while (max > 0) { r.push(+v.slice(min, max)); min -= l; if (min < 0) min = 0; max -= l } trim(r); return new BigInteger(r, sign) } function parseNumberValue(v) { if (isPrecise(v)) { if (v !== truncate(v)) throw new Error(v + " is not an integer."); return new SmallInteger(v) } return parseStringValue(v.toString()) } function parseValue(v) { if (typeof v === "number") { return parseNumberValue(v) } if (typeof v === "string") { return parseStringValue(v) } return v } for (var i = 0; i < 1e3; i++) { Integer[i] = new SmallInteger(i); if (i > 0) Integer[-i] = new SmallInteger(-i) } Integer.one = Integer[1]; Integer.zero = Integer[0]; Integer.minusOne = Integer[-1]; Integer.max = max; Integer.min = min; Integer.gcd = gcd; Integer.lcm = lcm; Integer.isInstance = function (x) { return x instanceof BigInteger || x instanceof SmallInteger }; Integer.randBetween = randBetween; Integer.fromArray = function (digits, base, isNegative) { return parseBaseFromArray(digits.map(parseValue), parseValue(base || 10), isNegative) }; return Integer }();
"use strict";
function main(input) {
    const X = bigInt(input.replace("\n", ""));
    let cur = bigInt(100);
    let ans = 0;
    while (cur < X) {
        ans++;
        cur = cur.add(cur.divide(100));
    }
    console.log(ans);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));


Measured memory_bytes: 35448