/*
 * Copyright 2014 Jason Randolph Eads
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

/*
 * Author: Jason R. Eads <jeads442@gmail.com> (c) 2014
 * Collects the product of all but the index for each slot
 */

// Normally you would just "var Long = require("long");" this....
// start LONG - source:https://github.com/dcodeIO/Long.js/blob/master/src/Long.js
/*
 Copyright 2013 Daniel Wirtz <dcode@dcode.io>
 Copyright 2009 The Closure Library Authors. All Rights Reserved.
 Licensed under the Apache License, Version 2.0 (the "License");
 you may not use this file except in compliance with the License.
 You may obtain a copy of the License at
 http://www.apache.org/licenses/LICENSE-2.0
 Unless required by applicable law or agreed to in writing, software
 distributed under the License is distributed on an "AS-IS" BASIS,
 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 */
/**
 * @license Long.js (c) 2013 Daniel Wirtz <dcode@dcode.io>
 * Released under the Apache License, Version 2.0
 * see: https://github.com/dcodeIO/Long.js for details
 */
//(function(global) {
// "use strict";
/**
 * Constructs a 64 bit two's-complement integer, given its low and high 32 bit values as *signed* integers.
 * See the from* functions below for more convenient ways of constructing Longs.
 * @exports Long
 * @class A Long class for representing a 64 bit two's-complement integer value.
 * @param {number} low The low (signed) 32 bits of the long
 * @param {number} high The high (signed) 32 bits of the long
 * @param {boolean=} unsigned Whether unsigned or not, defaults to `false` for signed
 * @constructor
 */
 var Long = function(low, high, unsigned) {
/**
 * The low 32 bits as a signed value.
 * @type {number}
 * @expose
 */
 this.low = low|0;
/**
 * The high 32 bits as a signed value.
 * @type {number}
 * @expose
 */
 this.high = high|0;
/**
 * Whether unsigned or not.
 * @type {boolean}
 * @expose
 */
 this.unsigned = !!unsigned;
 };
 // The internal representation of a long is the two given signed, 32-bit values.
 // We use 32-bit pieces because these are the size of integers on which
 // Javascript performs bit-operations. For operations like addition and
 // multiplication, we split each number into 16 bit pieces, which can easily be
 // multiplied within Javascript's floating-point representation without overflow
 // or change in sign.
 //
 // In the algorithms below, we frequently reduce the negative case to the
 // positive case by negating the input(s) and then post-processing the result.
 // Note that we must ALWAYS check specially whether those values are MIN_VALUE
 // (-2^63) because -MIN_VALUE == MIN_VALUE (since 2^63 cannot be represented as
 // a positive number, it overflows back into a negative). Not handling this
 // case would often result in infinite recursion.
 //
 // Common constant values ZERO, ONE, NEG_ONE, etc. are defined below the from*
 // methods on which they depend.
/**
 * Tests if the specified object is a Long.
 * @param {*} obj Object
 * @returns {boolean}
 * @expose
 */
 Long.isLong = function(obj) {
 return (obj && obj instanceof Long) === true;
 };
/**
 * A cache of the Long representations of small integer values.
 * @type {!Object}
 * @inner
 */
 var INT_CACHE = {};
/**
 * A cache of the Long representations of small unsigned integer values.
 * @type {!Object}
 * @inner
 */
 var UINT_CACHE = {};
/**
 * Returns a Long representing the given 32 bit integer value.
 * @param {number} value The 32 bit integer in question
 * @param {boolean=} unsigned Whether unsigned or not, defaults to `false` for signed
 * @returns {!Long} The corresponding Long value
 * @expose
 */
 Long.fromInt = function(value, unsigned) {
 var obj, cachedObj;
 if (!unsigned) {
 value = value | 0;
 if (-128 <= value && value < 128) {
 cachedObj = INT_CACHE[value];
 if (cachedObj)
 return cachedObj;
 }
 obj = new Long(value, value < 0 ? -1 : 0, false);
 if (-128 <= value && value < 128)
 INT_CACHE[value] = obj;
 return obj;
 } else {
 value = value >>> 0;
 if (0 <= value && value < 256) {
 cachedObj = UINT_CACHE[value];
 if (cachedObj)
 return cachedObj;
 }
 obj = new Long(value, (value | 0) < 0 ? -1 : 0, true);
 if (0 <= value && value < 256)
 UINT_CACHE[value] = obj;
 return obj;
 }
 };
/**
 * Returns a Long representing the given value, provided that it is a finite number. Otherwise, zero is returned.
 * @param {number} value The number in question
 * @param {boolean=} unsigned Whether unsigned or not, defaults to `false` for signed
 * @returns {!Long} The corresponding Long value
 * @expose
 */
 Long.fromNumber = function(value, unsigned) {
 unsigned = !!unsigned;
 if (isNaN(value) || !isFinite(value))
 return Long.ZERO;
 if (!unsigned && value <= -TWO_PWR_63_DBL)
 return Long.MIN_VALUE;
 if (!unsigned && value + 1 >= TWO_PWR_63_DBL)
 return Long.MAX_VALUE;
 if (unsigned && value >= TWO_PWR_64_DBL)
 return Long.MAX_UNSIGNED_VALUE;
 if (value < 0)
 return Long.fromNumber(-value, unsigned).negate();
 return new Long((value % TWO_PWR_32_DBL) | 0, (value / TWO_PWR_32_DBL) | 0, unsigned);
 };
/**
 * Returns a Long representing the 64 bit integer that comes by concatenating the given low and high bits. Each is
 * assumed to use 32 bits.
 * @param {number} lowBits The low 32 bits
 * @param {number} highBits The high 32 bits
 * @param {boolean=} unsigned Whether unsigned or not, defaults to `false` for signed
 * @returns {!Long} The corresponding Long value
 * @expose
 */
 Long.fromBits = function(lowBits, highBits, unsigned) {
 return new Long(lowBits, highBits, unsigned);
 };
/**
 * Returns a Long representation of the given string, written using the specified radix.
 * @param {string} str The textual representation of the Long
 * @param {(boolean|number)=} unsigned Whether unsigned or not, defaults to `false` for signed
 * @param {number=} radix The radix in which the text is written (2-36), defaults to 10
 * @returns {!Long} The corresponding Long value
 * @expose
 */
 Long.fromString = function(str, unsigned, radix) {
 if (str.length === 0)
 throw Error('number format error: empty string');
 if (str === "NaN" || str === "Infinity" || str === "+Infinity" || str === "-Infinity")
 return Long.ZERO;
 if (typeof unsigned === 'number') // For goog.math.long compatibility
 radix = unsigned,
 unsigned = false;
 radix = radix || 10;
 if (radix < 2 || 36 < radix)
 throw Error('radix out of range: ' + radix);
 var p;
 if ((p = str.indexOf('-')) > 0)
 throw Error('number format error: interior "-" character: ' + str);
 else if (p === 0)
 return Long.fromString(str.substring(1), unsigned, radix).negate();
 // Do several (8) digits each time through the loop, so as to
 // minimize the calls to the very expensive emulated div.
 var radixToPower = Long.fromNumber(Math.pow(radix, 8));
 var result = Long.ZERO;
 for (var i = 0; i < str.length; i += 8) {
 var size = Math.min(8, str.length - i);
 var value = parseInt(str.substring(i, i + size), radix);
 if (size < 8) {
 var power = Long.fromNumber(Math.pow(radix, size));
 result = result.multiply(power).add(Long.fromNumber(value));
 } else {
 result = result.multiply(radixToPower);
 result = result.add(Long.fromNumber(value));
 }
 }
 result.unsigned = unsigned;
 return result;
 };
/**
 * Converts the specified value to a Long.
 * @param {!Long|number|string|!{low: number, high: number, unsigned: boolean}} val Value
 * @returns {!Long}
 * @expose
 */
 Long.fromValue = function(val) {
 if (typeof val === 'number')
 return Long.fromNumber(val);
 if (typeof val === 'string')
 return Long.fromString(val);
 if (Long.isLong(val))
 return val;
 // Throws for not an object (undefined, null):
 return new Long(val.low, val.high, val.unsigned);
 };
 // NOTE: the compiler should inline these constant values below and then remove these variables, so there should be
 // no runtime penalty for these.
/**
 * @type {number}
 * @inner
 */
 var TWO_PWR_16_DBL = 1 << 16;
/**
 * @type {number}
 * @inner
 */
 var TWO_PWR_24_DBL = 1 << 24;
/**
 * @type {number}
 * @inner
 */
 var TWO_PWR_32_DBL = TWO_PWR_16_DBL * TWO_PWR_16_DBL;
/**
 * @type {number}
 * @inner
 */
 var TWO_PWR_31_DBL = TWO_PWR_32_DBL / 2;
/**
 * @type {number}
 * @inner
 */
 var TWO_PWR_48_DBL = TWO_PWR_32_DBL * TWO_PWR_16_DBL;
/**
 * @type {number}
 * @inner
 */
 var TWO_PWR_64_DBL = TWO_PWR_32_DBL * TWO_PWR_32_DBL;
/**
 * @type {number}
 * @inner
 */
 var TWO_PWR_63_DBL = TWO_PWR_64_DBL / 2;
/**
 * @type {!Long}
 * @inner
 */
 var TWO_PWR_24 = Long.fromInt(1 << 24);
/**
 * Signed zero.
 * @type {!Long}
 * @expose
 */
 Long.ZERO = Long.fromInt(0);
/**
 * Unsigned zero.
 * @type {!Long}
 * @expose
 */
 Long.UZERO = Long.fromInt(0, true);
/**
 * Signed one.
 * @type {!Long}
 * @expose
 */
 Long.ONE = Long.fromInt(1);
/**
 * Unsigned one.
 * @type {!Long}
 * @expose
 */
 Long.UONE = Long.fromInt(1, true);
/**
 * Signed negative one.
 * @type {!Long}
 * @expose
 */
 Long.NEG_ONE = Long.fromInt(-1);
/**
 * Maximum signed value.
 * @type {!Long}
 * @expose
 */
 Long.MAX_VALUE = Long.fromBits(0xFFFFFFFF|0, 0x7FFFFFFF|0, false);
/**
 * Maximum unsigned value.
 * @type {!Long}
 * @expose
 */
 Long.MAX_UNSIGNED_VALUE = Long.fromBits(0xFFFFFFFF|0, 0xFFFFFFFF|0, true);
/**
 * Minimum signed value.
 * @type {!Long}
 * @expose
 */
 Long.MIN_VALUE = Long.fromBits(0, 0x80000000|0, false);
/**
 * Converts the Long to a 32 bit integer, assuming it is a 32 bit integer.
 * @returns {number}
 * @expose
 */
 Long.prototype.toInt = function() {
 return this.unsigned ? this.low >>> 0 : this.low;
 };
/**
 * Converts the Long to a the nearest floating-point representation of this value (double, 53 bit mantissa).
 * @returns {number}
 * @expose
 */
 Long.prototype.toNumber = function() {
 if (this.unsigned) {
 return ((this.high >>> 0) * TWO_PWR_32_DBL) + (this.low >>> 0);
 }
 return this.high * TWO_PWR_32_DBL + (this.low >>> 0);
 };
/**
 * Converts the Long to a string written in the specified radix.
 * @param {number=} radix Radix (2-36), defaults to 10
 * @returns {string}
 * @override
 * @throws {RangeError} If `radix` is out of range
 * @expose
 */
 Long.prototype.toString = function(radix) {
 radix = radix || 10;
 if (radix < 2 || 36 < radix)
 throw RangeError('radix out of range: ' + radix);
 if (this.isZero())
 return '0';
 var rem;
 if (this.isNegative()) { // Unsigned Longs are never negative
 if (this.equals(Long.MIN_VALUE)) {
 // We need to change the Long value before it can be negated, so we remove
 // the bottom-most digit in this base and then recurse to do the rest.
 var radixLong = Long.fromNumber(radix);
 var div = this.div(radixLong);
 rem = div.multiply(radixLong).subtract(this);
 return div.toString(radix) + rem.toInt().toString(radix);
 } else
 return '-' + this.negate().toString(radix);
 }
 // Do several (6) digits each time through the loop, so as to
 // minimize the calls to the very expensive emulated div.
 var radixToPower = Long.fromNumber(Math.pow(radix, 6), this.unsigned);
 rem = this;
 var result = '';
 while (true) {
 var remDiv = rem.div(radixToPower),
 intval = rem.subtract(remDiv.multiply(radixToPower)).toInt() >>> 0,
 digits = intval.toString(radix);
 rem = remDiv;
 if (rem.isZero())
 return digits + result;
 else {
 while (digits.length < 6)
 digits = '0' + digits;
 result = '' + digits + result;
 }
 }
 };
/**
 * Gets the high 32 bits as a signed integer.
 * @returns {number} Signed high bits
 * @expose
 */
 Long.prototype.getHighBits = function() {
 return this.high;
 };
/**
 * Gets the high 32 bits as an unsigned integer.
 * @returns {number} Unsigned high bits
 * @expose
 */
 Long.prototype.getHighBitsUnsigned = function() {
 return this.high >>> 0;
 };
/**
 * Gets the low 32 bits as a signed integer.
 * @returns {number} Signed low bits
 * @expose
 */
 Long.prototype.getLowBits = function() {
 return this.low;
 };
/**
 * Gets the low 32 bits as an unsigned integer.
 * @returns {number} Unsigned low bits
 * @expose
 */
 Long.prototype.getLowBitsUnsigned = function() {
 return this.low >>> 0;
 };
/**
 * Gets the number of bits needed to represent the absolute value of this Long.
 * @returns {number}
 * @expose
 */
 Long.prototype.getNumBitsAbs = function() {
 if (this.isNegative()) // Unsigned Longs are never negative
 return this.equals(Long.MIN_VALUE) ? 64 : this.negate().getNumBitsAbs();
 var val = this.high != 0 ? this.high : this.low;
 for (var bit = 31; bit > 0; bit--)
 if ((val & (1 << bit)) != 0)
 break;
 return this.high != 0 ? bit + 33 : bit + 1;
 };
/**
 * Tests if this Long's value equals zero.
 * @returns {boolean}
 * @expose
 */
 Long.prototype.isZero = function() {
 return this.high === 0 && this.low === 0;
 };
/**
 * Tests if this Long's value is negative.
 * @returns {boolean}
 * @expose
 */
 Long.prototype.isNegative = function() {
 return !this.unsigned && this.high < 0;
 };
/**
 * Tests if this Long's value is positive.
 * @returns {boolean}
 * @expose
 */
 Long.prototype.isPositive = function() {
 return this.unsigned || this.high >= 0;
 };
/**
 * Tests if this Long's value is odd.
 * @returns {boolean}
 * @expose
 */
 Long.prototype.isOdd = function() {
 return (this.low & 1) === 1;
 };
/**
 * Tests if this Long's value is even.
 * @returns {boolean}
 */
 Long.prototype.isEven = function() {
 return (this.low & 1) === 0;
 };
/**
 * Tests if this Long's value equals the specified's.
 * @param {!Long|number|string} other Other value
 * @returns {boolean}
 * @expose
 */
 Long.prototype.equals = function(other) {
 if (!Long.isLong(other))
 other = Long.fromValue(other);
 if (this.unsigned !== other.unsigned && (this.high >>> 31) === 1 && (other.high >>> 31) === 1)
 return false;
 return this.high === other.high && this.low === other.low;
 };
/**
 * Tests if this Long's value differs from the specified's.
 * @param {!Long|number|string} other Other value
 * @returns {boolean}
 * @expose
 */
 Long.prototype.notEquals = function(other) {
 if (!Long.isLong(other))
 other = Long.fromValue(other);
 return !this.equals(other);
 };
/**
 * Tests if this Long's value is less than the specified's.
 * @param {!Long|number|string} other Other value
 * @returns {boolean}
 * @expose
 */
 Long.prototype.lessThan = function(other) {
 if (!Long.isLong(other))
 other = Long.fromValue(other);
 return this.compare(other) < 0;
 };
/**
 * Tests if this Long's value is less than or equal the specified's.
 * @param {!Long|number|string} other Other value
 * @returns {boolean}
 * @expose
 */
 Long.prototype.lessThanOrEqual = function(other) {
 if (!Long.isLong(other))
 other = Long.fromValue(other);
 return this.compare(other) <= 0;
 };
/**
 * Tests if this Long's value is greater than the specified's.
 * @param {!Long|number|string} other Other value
 * @returns {boolean}
 * @expose
 */
 Long.prototype.greaterThan = function(other) {
 if (!Long.isLong(other))
 other = Long.fromValue(other);
 return this.compare(other) > 0;
 };
/**
 * Tests if this Long's value is greater than or equal the specified's.
 * @param {!Long|number|string} other Other value
 * @returns {boolean}
 * @expose
 */
 Long.prototype.greaterThanOrEqual = function(other) {
 return this.compare(other) >= 0;
 };
/**
 * Compares this Long's value with the specified's.
 * @param {!Long|number|string} other Other value
 * @returns {number} 0 if they are the same, 1 if the this is greater and -1
 * if the given one is greater
 * @expose
 */
 Long.prototype.compare = function(other) {
 if (this.equals(other)) {
 return 0;
 }
 var thisNeg = this.isNegative();
 var otherNeg = other.isNegative();
 if (thisNeg && !otherNeg) return -1;
 if (!thisNeg && otherNeg) return 1;
 // At this point the sign bits are the same
 if (!this.unsigned)
 return this.subtract(other).isNegative() ? -1 : 1;
 // Both are positive if at least one is unsigned
 return (other.high >>> 0) > (this.high >>> 0) || (other.high === this.high && (other.low >>> 0) > (this.low >>> 0)) ? -1 : 1;
 };
/**
 * Negates this Long's value.
 * @returns {!Long} Negated Long
 * @expose
 */
 Long.prototype.negate = function() {
 if (!this.unsigned && this.equals(Long.MIN_VALUE))
 return Long.MIN_VALUE;
 return this.not().add(Long.ONE);
 };
/**
 * Returns the sum of this and the specified Long.
 * @param {!Long|number|string} addend Addend
 * @returns {!Long} Sum
 * @expose
 */
 Long.prototype.add = function(addend) {
 if (!Long.isLong(addend))
 addend = Long.fromValue(addend);
 // Divide each number into 4 chunks of 16 bits, and then sum the chunks.
 var a48 = this.high >>> 16;
 var a32 = this.high & 0xFFFF;
 var a16 = this.low >>> 16;
 var a00 = this.low & 0xFFFF;
 var b48 = addend.high >>> 16;
 var b32 = addend.high & 0xFFFF;
 var b16 = addend.low >>> 16;
 var b00 = addend.low & 0xFFFF;
 var c48 = 0, c32 = 0, c16 = 0, c00 = 0;
 c00 += a00 + b00;
 c16 += c00 >>> 16;
 c00 &= 0xFFFF;
 c16 += a16 + b16;
 c32 += c16 >>> 16;
 c16 &= 0xFFFF;
 c32 += a32 + b32;
 c48 += c32 >>> 16;
 c32 &= 0xFFFF;
 c48 += a48 + b48;
 c48 &= 0xFFFF;
 return Long.fromBits((c16 << 16) | c00, (c48 << 16) | c32, this.unsigned);
 };
/**
 * Returns the difference of this and the specified Long.
 * @param {!Long|number|string} subtrahend Subtrahend
 * @returns {!Long} Difference
 * @expose
 */
 Long.prototype.subtract = function(subtrahend) {
 if (!Long.isLong(subtrahend))
 subtrahend = Long.fromValue(subtrahend);
 return this.add(subtrahend.negate());
 };
/**
 * Returns the product of this and the specified Long.
 * @param {!Long|number|string} multiplier Multiplier
 * @returns {!Long} Product
 * @expose
 */
 Long.prototype.multiply = function(multiplier) {
 if (this.isZero())
 return Long.ZERO;
 if (!Long.isLong(multiplier))
 multiplier = Long.fromValue(multiplier);
 if (multiplier.isZero())
 return Long.ZERO;
 if (this.equals(Long.MIN_VALUE))
 return multiplier.isOdd() ? Long.MIN_VALUE : Long.ZERO;
 if (multiplier.equals(Long.MIN_VALUE))
 return this.isOdd() ? Long.MIN_VALUE : Long.ZERO;
 if (this.isNegative()) {
 if (multiplier.isNegative())
 return this.negate().multiply(multiplier.negate());
 else
 return this.negate().multiply(multiplier).negate();
 } else if (multiplier.isNegative())
 return this.multiply(multiplier.negate()).negate();
 // If both longs are small, use float multiplication
 if (this.lessThan(TWO_PWR_24) && multiplier.lessThan(TWO_PWR_24))
 return Long.fromNumber(this.toNumber() * multiplier.toNumber(), this.unsigned);
 // Divide each long into 4 chunks of 16 bits, and then add up 4x4 products.
 // We can skip products that would overflow.
 var a48 = this.high >>> 16;
 var a32 = this.high & 0xFFFF;
 var a16 = this.low >>> 16;
 var a00 = this.low & 0xFFFF;
 var b48 = multiplier.high >>> 16;
 var b32 = multiplier.high & 0xFFFF;
 var b16 = multiplier.low >>> 16;
 var b00 = multiplier.low & 0xFFFF;
 var c48 = 0, c32 = 0, c16 = 0, c00 = 0;
 c00 += a00 * b00;
 c16 += c00 >>> 16;
 c00 &= 0xFFFF;
 c16 += a16 * b00;
 c32 += c16 >>> 16;
 c16 &= 0xFFFF;
 c16 += a00 * b16;
 c32 += c16 >>> 16;
 c16 &= 0xFFFF;
 c32 += a32 * b00;
 c48 += c32 >>> 16;
 c32 &= 0xFFFF;
 c32 += a16 * b16;
 c48 += c32 >>> 16;
 c32 &= 0xFFFF;
 c32 += a00 * b32;
 c48 += c32 >>> 16;
 c32 &= 0xFFFF;
 c48 += a48 * b00 + a32 * b16 + a16 * b32 + a00 * b48;
 c48 &= 0xFFFF;
 return Long.fromBits((c16 << 16) | c00, (c48 << 16) | c32, this.unsigned);
 };
/**
 * Returns this Long divided by the specified.
 * @param {!Long|number|string} divisor Divisor
 * @returns {!Long} Quotient
 * @expose
 */
 Long.prototype.div = function(divisor) {
 if (!Long.isLong(divisor))
 divisor = Long.fromValue(divisor);
 if (divisor.isZero())
 throw(new Error('division by zero'));
 if (this.isZero())
 return this.unsigned ? Long.UZERO : Long.ZERO;
 var approx, rem, res;
 if (this.equals(Long.MIN_VALUE)) {
 if (divisor.equals(Long.ONE) || divisor.equals(Long.NEG_ONE))
 return Long.MIN_VALUE; // recall that -MIN_VALUE == MIN_VALUE
 else if (divisor.equals(Long.MIN_VALUE))
 return Long.ONE;
 else {
 // At this point, we have |other| >= 2, so |this/other| < |MIN_VALUE|.
 var halfThis = this.shiftRight(1);
 approx = halfThis.div(divisor).shiftLeft(1);
 if (approx.equals(Long.ZERO)) {
 return divisor.isNegative() ? Long.ONE : Long.NEG_ONE;
 } else {
 rem = this.subtract(divisor.multiply(approx));
 res = approx.add(rem.div(divisor));
 return res;
 }
 }
 } else if (divisor.equals(Long.MIN_VALUE))
 return this.unsigned ? Long.UZERO : Long.ZERO;
 if (this.isNegative()) {
 if (divisor.isNegative())
 return this.negate().div(divisor.negate());
 return this.negate().div(divisor).negate();
 } else if (divisor.isNegative())
 return this.div(divisor.negate()).negate();
 // Repeat the following until the remainder is less than other: find a
 // floating-point that approximates remainder / other *from below*, add this
 // into the result, and subtract it from the remainder. It is critical that
 // the approximate value is less than or equal to the real value so that the
 // remainder never becomes negative.
 res = Long.ZERO;
 rem = this;
 while (rem.greaterThanOrEqual(divisor)) {
 // Approximate the result of division. This may be a little greater or
 // smaller than the actual value.
 approx = Math.max(1, Math.floor(rem.toNumber() / divisor.toNumber()));
 // We will tweak the approximate result by changing it in the 48-th digit or
 // the smallest non-fractional digit, whichever is larger.
 var log2 = Math.ceil(Math.log(approx) / Math.LN2),
 delta = (log2 <= 48) ? 1 : Math.pow(2, log2 - 48),
 // Decrease the approximation until it is smaller than the remainder. Note
 // that if it is too large, the product overflows and is negative.
 approxRes = Long.fromNumber(approx),
 approxRem = approxRes.multiply(divisor);
 while (approxRem.isNegative() || approxRem.greaterThan(rem)) {
 approx -= delta;
 approxRes = Long.fromNumber(approx, this.unsigned);
 approxRem = approxRes.multiply(divisor);
 }
 // We know the answer can't be zero... and actually, zero would cause
 // infinite recursion since we would make no progress.
 if (approxRes.isZero())
 approxRes = Long.ONE;
 res = res.add(approxRes);
 rem = rem.subtract(approxRem);
 }
 return res;
 };
/**
 * Returns this Long modulo the specified.
 * @param {!Long|number|string} divisor Divisor
 * @returns {!Long} Remainder
 * @expose
 */
 Long.prototype.modulo = function(divisor) {
 if (!Long.isLong(divisor))
 divisor = Long.fromValue(divisor);
 return this.subtract(this.div(divisor).multiply(divisor));
 };
/**
 * Returns the bitwise NOT of this Long.
 * @returns {!Long}
 * @expose
 */
 Long.prototype.not = function() {
 return Long.fromBits(~this.low, ~this.high, this.unsigned);
 };
/**
 * Returns the bitwise AND of this Long and the specified.
 * @param {!Long|number|string} other Other Long
 * @returns {!Long}
 * @expose
 */
 Long.prototype.and = function(other) {
 if (!Long.isLong(other))
 other = Long.fromValue(other);
 return Long.fromBits(this.low & other.low, this.high & other.high, this.unsigned);
 };
/**
 * Returns the bitwise OR of this Long and the specified.
 * @param {!Long|number|string} other Other Long
 * @returns {!Long}
 * @expose
 */
 Long.prototype.or = function(other) {
 if (!Long.isLong(other))
 other = Long.fromValue(other);
 return Long.fromBits(this.low | other.low, this.high | other.high, this.unsigned);
 };
/**
 * Returns the bitwise XOR of this Long and the given one.
 * @param {!Long|number|string} other Other Long
 * @returns {!Long}
 * @expose
 */
 Long.prototype.xor = function(other) {
 if (!Long.isLong(other))
 other = Long.fromValue(other);
 return Long.fromBits(this.low ^ other.low, this.high ^ other.high, this.unsigned);
 };
/**
 * Returns this Long with bits shifted to the left by the given amount.
 * @param {number|!Long} numBits Number of bits
 * @returns {!Long} Shifted Long
 * @expose
 */
 Long.prototype.shiftLeft = function(numBits) {
 if (Long.isLong(numBits))
 numBits = numBits.toInt();
 if ((numBits &= 63) === 0)
 return this;
 else if (numBits < 32)
 return Long.fromBits(this.low << numBits, (this.high << numBits) | (this.low >>> (32 - numBits)), this.unsigned);
 else
 return Long.fromBits(0, this.low << (numBits - 32), this.unsigned);
 };
/**
 * Returns this Long with bits arithmetically shifted to the right by the given amount.
 * @param {number|!Long} numBits Number of bits
 * @returns {!Long} Shifted Long
 * @expose
 */
 Long.prototype.shiftRight = function(numBits) {
 if (Long.isLong(numBits))
 numBits = numBits.toInt();
 if ((numBits &= 63) === 0)
 return this;
 else if (numBits < 32)
 return Long.fromBits((this.low >>> numBits) | (this.high << (32 - numBits)), this.high >> numBits, this.unsigned);
 else
 return Long.fromBits(this.high >> (numBits - 32), this.high >= 0 ? 0 : -1, this.unsigned);
 };
/**
 * Returns this Long with bits logically shifted to the right by the given amount.
 * @param {number|!Long} numBits Number of bits
 * @returns {!Long} Shifted Long
 * @expose
 */
 Long.prototype.shiftRightUnsigned = function(numBits) {
 if (Long.isLong(numBits))
 numBits = numBits.toInt();
 numBits &= 63;
 if (numBits === 0)
 return this;
 else {
 var high = this.high;
 if (numBits < 32) {
 var low = this.low;
 return Long.fromBits((low >>> numBits) | (high << (32 - numBits)), high >>> numBits, this.unsigned);
 } else if (numBits === 32)
 return Long.fromBits(high, 0, this.unsigned);
 else
 return Long.fromBits(high >>> (numBits - 32), 0, this.unsigned);
 }
 };
/**
 * Converts this Long to signed.
 * @returns {!Long} Signed long
 * @expose
 */
 Long.prototype.toSigned = function() {
 if (!this.unsigned)
 return this;
 return new Long(this.low, this.high, false);
 };
/**
 * Converts this Long to unsigned.
 * @returns {!Long} Unsigned long
 * @expose
 */
 Long.prototype.toUnsigned = function() {
 if (this.unsigned)
 return this;
 return new Long(this.low, this.high, true);
 };
/* CommonJS */ if (typeof require === 'function' && typeof module === 'object' && module && module.id && typeof exports === 'object' && exports)
 module["exports"] = Long;
/* AMD */ else if (typeof define === 'function' && define["amd"])
 define(function() { return Long; });
/* Global */ else
 (global["dcodeIO"] = global["dcodeIO"] || {})["Long"] = Long;
// })(this);
// end LONG

// start INPUT - soucre: https://www.interviewstreet.com/recruit/challenges/faq/view
process.stdin.resume();
process.stdin.setEncoding("ascii");
var input = "";
process.stdin.on("data", function (chunk) {
				 input += chunk;
				 });
process.stdin.on("end", solve);
// end INPUT

function solve() {
	var numbers = cleanInput(input);

	// coerce newline(s) and convert to numbers
	function cleanInput( input ) {
		var ret = [];
		var clean = input.trim().replace(/\n/g,' ').split(' ');
		clean = clean.slice(1,clean.length);
		for( c in clean ) {
			ret.push(Long.fromString(clean[c]));
		}
		return ret;
	}
	
	// For each element, trace out the solution
	tree = buildTree(numbers);
	products = [];
	
	for (n in numbers) {
		console.log(traceTree(tree, n).toString());
	}

	// Builds a special node tree which can be parsed quickly for answers
	function buildTree(values) {
		var levels = [];
		levels.push([]);
		
		// First layer is created raw from input
		for (v in values) {
			var node = {};
			node.keys = [v];
			node.value = values[v];
			levels[0].push(node);
		}
		// Now create the layers above
		indexL = 0; // The level we're building on
		indexA = 1; // The level we're building
		while (levels[indexL].length > 1) {
			levels.push([]);
			
			// combine the elements from below
			for (i = 0; i < levels[indexL].length; i++) {
				if (levels[indexL][i] !== undefined) {
					// At least one node below...
					
					var node = {};
					if (levels[indexL][i + 1] !== undefined) {
						// Two nodes below. Combine.
						node.keys = levels[indexL][i].keys.concat(levels[indexL][i + 1].keys);
						node.value = levels[indexL][i].value.multiply(levels[indexL][i + 1].value);
						node.left = levels[indexL][i];
						node.right = levels[indexL][i + 1];
						i++;
					}
					else {
						// Only one node below. Pass up tree.
						node.keys = levels[indexL][i].keys.concat([]);
						node.value = levels[indexL][i].value;
						node.left = levels[indexL][i];
					}
					levels[indexA].push(node);
				}
			}
			indexL = indexA;
			indexA++;
		}
		return levels[indexL][0];
	}
	// Walk down from the top of the tree, excluding an index while multiplying
	function traceTree(tree, index) {
		function keyMatch(node, index) {
			if ((node.keys).indexOf(index) != -1) {
				return true;
			}
			return false;
		}
		
		function traceNode(node, index) {
			if (node.right === undefined) {
				// Either at bottom or on fully collapsed track
				if(node.left === undefined) {
					// Made it all the way down...
					return Long.ONE;
				}
				else {
					// Track down left to prevent orpahed nodes
					return traceNode(node.left, index);
				}
			}
			// One has the key, checking right...
			if (keyMatch(node.right, index)) {
				// and it has the key! Trace right and return left value.
				return traceNode(node.right, index).multiply(node.left.value);
			}
			else {
				// else trace the left and return right value.
				return traceNode(node.left, index).multiply(node.right.value);
			}
		}
		return traceNode(tree, index);
	}
}